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Which of the following statements about the orientation of a shape under rotation is TRUE?
A) Orientation is preserved only for $90^\circ$ rotations
B) Orientation is preserved
C) Orientation becomes random
D) Orientation is reversed
Correct answer: B) Orientation is preserved.
A rotation in the plane that maps a point $(x,y)$ to $(x,-y)$ is
A) not a rotation but a reflection
B) a rotation of $90^\circ$
C) a rotation of $270^\circ$
D) a rotation of $180^\circ$
Correct answer: A) not a rotation but a reflection.
To describe a rotation fully on a grid, you must specify
A) centre and angle only
B) angle and direction only
C) centre only
D) centre, angle and direction
Correct answer: D) centre, angle and direction.
Which rotation about the origin maps $(1,0)$ to $(0,1)$?
A) $90^\circ$ anticlockwise
B) $270^\circ$ anticlockwise
C) $90^\circ$ clockwise
D) $180^\circ$
Correct answer: A) $90^\circ$ anticlockwise.
If a shape has rotational symmetry of order $4$, what is the smallest angle that maps it onto itself?
A) $60^\circ$
B) $45^\circ$
C) $120^\circ$
D) $90^\circ$
Correct answer: D) $90^\circ$.
Which of the following transformations could be the result of two successive reflections in intersecting lines?
A) A shear
B) An enlargement
C) A rotation
D) A translation
Correct answer: C) A rotation.
If a rotation maps point $P$ to $P'$ and the centre is $O$, what is true about $OP$ and $OP'$?
A) They are perpendicular
B) $OP = OP'$
C) $OP < OP'$
D) $OP > OP'$
Correct answer: B) $OP = OP'$.
When a shape is rotated $180^\circ$ about its centre, which points are invariant?
A) Points at the centre of rotation
B) All points of the shape
C) No points at all
D) Only vertices
Correct answer: A) Points at the centre of rotation.
A translation in the plane can be represented by
A) a reflection line
B) a column vector
C) a single number
D) a diagonal matrix only
Correct answer: B) a column vector.
The translation by vector $\begin{pmatrix} a \\ b \end{pmatrix}$ maps $(x,y)$ to
A) $(x, y)$
B) $(x-a, y-b)$
C) $(x+a, y+b)$
D) $(ax, by)$
Correct answer: C) $(x+a, y+b)$.
Which property is TRUE for all translations?
A) Distances between points change
B) All points move the same distance in the same direction
C) Some points remain fixed
D) Angles between line segments change
Correct answer: B) All points move the same distance in the same direction.
Which point(s) remain invariant under a non-zero translation?
A) Only the origin
B) All points
C) Only points on the $x$-axis
D) No points
Correct answer: D) No points.
The translation by $\begin{pmatrix} 0 \\ -3 \end{pmatrix}$ moves a point
A) down by $3$ units
B) left by $3$ units
C) right by $3$ units
D) up by $3$ units
Correct answer: A) down by $3$ units.
Which vector represents a translation $3$ units to the right and $2$ units up?
A) $\begin{pmatrix} -3 \\ 2 \end{pmatrix}$
B) $\begin{pmatrix} 3 \\ -2 \end{pmatrix}$
C) $\begin{pmatrix} 2 \\ 3 \end{pmatrix}$
D) $\begin{pmatrix} 3 \\ 2 \end{pmatrix}$
Correct answer: D) $\begin{pmatrix} 3 \\ 2 \end{pmatrix}$.
If a shape is translated by $\begin{pmatrix} -4 \\ 0 \end{pmatrix}$, each point moves
A) 4 units left
B) 4 units down
C) 4 units right
D) 4 units up
Correct answer: A) 4 units left.
Which of the following describes the composition of two translations with vectors $\mathbf{u}$ and $\mathbf{v}$?
A) A reflection in a line
B) A rotation about the origin
C) An enlargement with scale factor $2$
D) A single translation by vector $\mathbf{u} + \mathbf{v}$
Correct answer: D) A single translation by vector $\mathbf{u} + \mathbf{v}$.
Under a translation by $\begin{pmatrix} 5 \\ -1 \end{pmatrix}$, the point $(2,3)$ maps to
A) $(3,4)$
B) $(2,-1)$
C) $(7,4)$
D) $(7,2)$
Correct answer: D) $(7,2)$.
If a translation maps $A(1,2)$ to $A'(4,6)$, what is the translation vector?
A) $\begin{pmatrix} 3 \\ 4 \end{pmatrix}$
B) $\begin{pmatrix} -3 \\ -4 \end{pmatrix}$
C) $\begin{pmatrix} 4 \\ 6 \end{pmatrix}$
D) $\begin{pmatrix} 1 \\ 2 \end{pmatrix}$
Correct answer: A) $\begin{pmatrix} 3 \\ 4 \end{pmatrix}$.
Translations preserve which of the following?
A) Size but not shape
B) Shape and size
C) Shape but not size
D) Neither shape nor size
Correct answer: B) Shape and size.
Which sequence of transformations is equivalent to a single translation?
A) A reflection followed by a rotation
B) Two reflections in intersecting lines
C) An enlargement followed by a reflection
D) Two translations one after the other
Correct answer: D) Two translations one after the other.
If the translation vector is $\begin{pmatrix} 0 \\ 0 \end{pmatrix}$, the transformation is
A) a reflection
B) the identity (no movement)
C) an enlargement
D) a rotation
Correct answer: B) the identity (no movement).
A translation that maps each vertex of a shape to itself is
A) a reflection in the $x$-axis
B) a rotation by $90^\circ$
C) an enlargement of scale factor $2$
D) the identity translation
Correct answer: D) the identity translation.
The image of a horizontal line under a translation is
A) a single point
B) another horizontal line
C) always a vertical line
D) a curve
Correct answer: B) another horizontal line.
The image of a vertical line under a translation is
A) always a horizontal line
B) another vertical line
C) a diagonal line through the origin
D) a circle
Correct answer: B) another vertical line.
Which of the following could model a translation in a real context?
A) Zooming in on a picture
B) Moving a shape across a screen without rotating it
C) Flipping a picture in a mirror
D) Turning a picture about a corner
Correct answer: B) Moving a shape across a screen without rotating it.
If a point moves from $(x,y)$ to $(x-2,y+5)$, the translation vector is
A) $\begin{pmatrix} -5 \\ 2 \end{pmatrix}$
B) $\begin{pmatrix} 5 \\ -2 \end{pmatrix}$
C) $\begin{pmatrix} -2 \\ 5 \end{pmatrix}$
D) $\begin{pmatrix} 2 \\ -5 \end{pmatrix}$
Correct answer: C) $\begin{pmatrix} -2 \\ 5 \end{pmatrix}$.
When describing a translation fully, you must give
A) the centre and angle
B) the scale factor and centre
C) the line of reflection
D) the translation vector
Correct answer: D) the translation vector.
For events $A$ and $B$, what does $P(A\text{ and }B)$ represent?
A) The probability that neither $A$ nor $B$ occurs
B) The probability that exactly one of $A$ and $B$ occurs
C) The probability that at least one of $A$ or $B$ occurs
D) The probability that both $A$ and $B$ occur
Correct answer: D) The probability that both $A$ and $B$ occur.
If events $A$ and $B$ are independent, which of the following must also be TRUE?
A) $P(A') = P(B')$
B) $P(A\text{ and }B) = 0$
C) $P(A\text{ or }B) = 1$
D) $P(A'\text{ and }B) = P(A')P(B)$
Correct answer: D) $P(A'\text{ and }B) = P(A')P(B)$.
A bag contains red, blue and green balls. Choosing one ball at random and then replacing it, and then choosing again, is an example of
A) independent repeated trials
B) mutually exclusive events
C) dependent repeated trials
D) impossible events
Correct answer: A) independent repeated trials.
To find the probability that at least one of two independent events occurs, one useful method is to compute
A) $P(A)P(B)$
B) $P(A)+P(B)$
C) $1-P(\text{neither event occurs})$
D) $P(A)-P(B)$
Correct answer: C) $1-P(\text{neither event occurs})$.
When rolling two dice, which event pair is independent?
A) "first die shows $3$" and "total is even"
B) "first die shows $6$" and "total is $12$"
C) "total is $2$" and "total is $12$"
D) "total is $7$" and "total is even"
Correct answer: A) "first die shows $3$" and "total is even".
If two events are mutually exclusive and exhaustive, what is $P(A\text{ or }B)$?
A) $P(A)+P(B)-1$
B) $1$
C) $0$
D) $P(A)P(B)$
Correct answer: B) $1$.
Two fair coins are tossed. What is the probability of getting exactly one head?
A) $\dfrac{1}{4}$
B) $\dfrac{3}{4}$
C) $\dfrac{1}{2}$
D) $\dfrac{1}{3}$
Correct answer: C) $\dfrac{1}{2}$.
Two fair coins are tossed. What is the probability of getting at least one head?
A) $\dfrac{1}{2}$
B) $\dfrac{1}{4}$
C) $\dfrac{2}{3}$
D) $\dfrac{3}{4}$
Correct answer: D) $\dfrac{3}{4}$.
If $P(A\text{ or }B)=0.8$, $P(A)=0.5$ and $P(B)=0.6$, what is $P(A\text{ and }B)$?
A) $0.8$
B) $0.1$
C) $1.1$
D) $0.3$
Correct answer: D) $0.3$.
An event "number is even" and an event "number is a multiple of $4$" when choosing a number from $1$ to $8$ are
A) dependent events
B) mutually exclusive events
C) complementary events
D) impossible events
Correct answer: A) dependent events.
The events $A$ and $A'$ are
A) complementary
B) independent but not complementary
C) mutually exclusive but not exhaustive
D) neither independent nor complementary
Correct answer: A) complementary.
If $P(A)=0.6$ and $P(A\text{ and }B)=0.3$, what is $P(B\mid A)$, the conditional probability of $B$ given $A$?
A) $0.3$
B) $\dfrac{0.3}{0.6}$
C) $0.6$
D) $0.9$
Correct answer: B) $\dfrac{0.3}{0.6}$.
If $A$ and $B$ are mutually exclusive, which equation is TRUE?
A) $P(A\text{ and }B) = P(A)+P(B)$
B) $P(A\text{ and }B) = 1$
C) $P(A\text{ and }B) = 0$
D) $P(A\text{ and }B) = P(A)P(B)$
Correct answer: C) $P(A\text{ and }B) = 0$.
If $P(A)=0.4$, $P(B)=0.3$ and $A$ and $B$ are mutually exclusive, what is $P(A\text{ or }B)$?
A) $0.7$
B) $0.4$
C) $0.12$
D) $0.1$
Correct answer: A) $0.7$.
Two events $A$ and $B$ are independent. Which statement is TRUE?
A) Their probabilities must be equal
B) They cannot happen together
C) The occurrence of one does not affect the probability of the other
D) Their probabilities must sum to $1$
Correct answer: C) The occurrence of one does not affect the probability of the other.
For events $A$ and $B$, what does $P(A\text{ or }B)$ represent?
A) The probability that neither occurs
B) The probability that both $A$ and $B$ occur
C) The probability that at least one of $A$ or $B$ occurs
D) The probability that exactly one does not occur
Correct answer: C) The probability that at least one of $A$ or $B$ occurs.
A card is drawn from a pack and not replaced, then a second card is drawn. These draws are an example of
A) independent events
B) mutually exclusive events
C) impossible events
D) dependent events
Correct answer: D) dependent events.
From a deck of $52$ cards, what is the probability of drawing a spade followed by a heart without replacement?
A) $\dfrac{13}{52} \times \dfrac{13}{51}$
B) $\dfrac{1}{52}$
C) $\dfrac{13}{51} \times \dfrac{12}{51}$
D) $\dfrac{1}{4} \times \dfrac{1}{4}$
Correct answer: A) $\dfrac{13}{52} \times \dfrac{13}{51}$.
Which of the following pairs of events from rolling a fair die is mutually exclusive?
A) "getting a $1$" and "getting an odd number"
B) "getting an even number" and "getting a number greater than $3$"
C) "getting a prime" and "getting an even number"
D) "getting a $2$" and "getting a $3$"
Correct answer: D) "getting a $2$" and "getting a $3$".
If $A$ and $B$ are independent, which equation is TRUE?
A) $P(A\text{ and }B) = P(A)P(B)$
B) $P(A\text{ and }B) = 0$
C) $P(A\text{ and }B) = P(A)+P(B)$
D) $P(A\text{ and }B) = P(A)-P(B)$
Correct answer: A) $P(A\text{ and }B) = P(A)P(B)$.
Which of the following is a reason to repeat an experiment many times?
A) To make the event become more likely
B) To ensure the probability becomes exactly $1$
C) To avoid using any fractions
D) To obtain a more reliable estimate of the probability
Correct answer: D) To obtain a more reliable estimate of the probability.
In an experiment with replacement, each trial is independent. What does this mean?
A) The outcome of one trial changes the next probabilities
B) The experiment cannot be repeated
C) The outcome of one trial does not affect the next
D) Only one outcome is possible
Correct answer: C) The outcome of one trial does not affect the next.
If an event never occurred in $80$ trials, what is its experimental probability?
A) $0.5$
B) $1$
C) $0$
D) $\dfrac{1}{80}$
Correct answer: C) $0$.
Which step is necessary to calculate an experimental probability?
A) Counting how often the event occurred and dividing by the total trials
B) Writing down the theoretical outcomes only
C) Choosing the most likely outcome by guesswork
D) Using a formula without doing any experiment
Correct answer: A) Counting how often the event occurred and dividing by the total trials.
In a game, a player wins if a spinner lands on a shaded region. After many spins, the experimental probability of winning is found to be close to $0.6$. What does this suggest?
A) Winning is impossible
B) The chance of winning is about $60\%$
C) The spinner is unfair in every possible way
D) Winning is certain
Correct answer: B) The chance of winning is about $60\%$.
If experimental probability is calculated as $0.48$ for an event, what is the corresponding percentage?
A) $0.48\%$
B) $48\%$
C) $4.8\%$
D) $52\%$
Correct answer: B) $48\%$.
A bag contains red and green counters. Without knowing how many of each, a student draws a counter, replaces it and repeats $100$ times, recording each result. What is the student trying to estimate?
A) The probability of drawing each colour
B) The exact numbers of counters in the bag
C) The size of the bag
D) The weight of the counters
Correct answer: A) The probability of drawing each colour.
The experimental probability of rain tomorrow is based on
A) a single person's opinion
B) past weather data and similar conditions
C) the number of days in a year
D) theoretical assumptions about dice
Correct answer: B) past weather data and similar conditions.
A class surveys how many students prefer each of four sports. Using the results to estimate the chance a randomly chosen student from the school prefers football is an example of
A) computing exact theoretical probability
B) using experimental data to estimate probability
C) ignoring relative frequencies
D) assuming all sports are equally popular
Correct answer: B) using experimental data to estimate probability.
If an event has experimental probability $0.3$ in $50$ trials, how many times did it occur?
A) $15$
B) $30$
C) $3$
D) $150$
Correct answer: A) $15$.
In an experiment, the experimental probability of an event is $0.2$. Out of $200$ trials, about how many times did the event occur?
A) $10$
B) $20$
C) $80$
D) $40$
Correct answer: D) $40$.
A spinner is spun $40$ times and lands on blue $18$ times. What is the relative frequency of landing on blue?
A) $\dfrac{40}{18}$
B) $\dfrac{22}{40}$
C) $\dfrac{18}{22}$
D) $\dfrac{18}{40}$
Correct answer: D) $\dfrac{18}{40}$.
As the number of trials increases, experimental probability tends to
A) move further away from the theoretical probability
B) stay at $0$
C) stay at $1$
D) get closer to the theoretical probability
Correct answer: D) get closer to the theoretical probability.
Why might experimental probability differ from theoretical probability in a small number of trials?
A) Theoretical probability is always wrong
B) Experimental probability cannot be calculated for small samples
C) Experimental probability ignores outcomes
D) Random variation can have a larger effect when there are few trials
Correct answer: D) Random variation can have a larger effect when there are few trials.
In an experiment, a six-sided die is rolled $60$ times and a $4$ appears $9$ times. Which statement is TRUE?
A) The die must be biased against $4$
B) The experimental probability of getting a $4$ is $\dfrac{9}{60}$
C) The theoretical probability is $\dfrac{9}{60}$
D) The experimental probability of getting a $4$ is $\dfrac{1}{6}$
Correct answer: B) The experimental probability of getting a $4$ is $\dfrac{9}{60}$.
A coin is tossed $50$ times and lands on heads $23$ times. What is the experimental probability of getting heads?
A) $\dfrac{27}{50}$
B) $\dfrac{23}{50}$
C) $\dfrac{50}{23}$
D) $\dfrac{23}{100}$
Correct answer: B) $\dfrac{23}{50}$.
Which formula correctly gives the experimental probability of an event?
A) $\dfrac{\text{number of possible outcomes}}{\text{number of trials}}$
B) $\dfrac{\text{number of times the event occurs}}{\text{total number of trials}}$
C) $\dfrac{\text{total number of trials}}{\text{number of times the event occurs}}$
D) $\dfrac{1}{\text{number of trials}}$
Correct answer: B) $\dfrac{\text{number of times the event occurs}}{\text{total number of trials}}$.
Experimental probability is based on
A) purely theoretical reasoning
B) results of actual trials or experiments
C) all possible outcomes only
D) guesswork without data
Correct answer: B) results of actual trials or experiments.
A student tosses two coins $100$ times and records the number of times they are both heads. What type of probability is the student estimating?
A) Experimental probability
B) Impossible probability
C) Subjective probability
D) Theoretical probability
Correct answer: A) Experimental probability.
If the probability that an event occurs is $p$, which expression gives the probability that it does not occur?
A) $p-1$
B) $1-p$
C) $\dfrac{1}{p}$
D) $p^{2}$
Correct answer: B) $1-p$.
Which probability represents an event that is very unlikely but still possible?
A) $1$
B) $0$
C) $0.9$
D) $0.05$
Correct answer: D) $0.05$.
Which of the following could be the probability of an event?
A) $0.7$
B) $-0.2$
C) $\dfrac{5}{4}$
D) $1.3$
Correct answer: A) $0.7$.
An event has probability $0.5$. Which description best matches this?
A) It is equally likely to happen as not happen
B) It is certain to happen
C) It is very unlikely
D) It is impossible
Correct answer: A) It is equally likely to happen as not happen.
Which probability describes an event that is impossible?
A) $1$
B) $0$
C) $\dfrac{3}{4}$
D) $0.5$
Correct answer: B) $0$.
Which of these cannot be the probability of an event?
A) $-\dfrac{1}{3}$
B) $0$
C) $1$
D) $\dfrac{2}{3}$
Correct answer: A) $-\dfrac{1}{3}$.
Which of the following lists probabilities in increasing order of likelihood?
A) $0.4,\;0.2,\;0.8,\;0$
B) $0.8,\;0.4,\;0.2,\;0$
C) $0.2,\;0,\;0.8,\;0.4$
D) $0,\;0.2,\;0.4,\;0.8$
Correct answer: D) $0,\;0.2,\;0.4,\;0.8$.
On a probability line from $0$ to $1$, where would a highly likely event be marked?
A) Exactly at $0$
B) Exactly at $0.5$
C) Closer to $0$ than to $0.5$
D) Closer to $1$ than to $0.5$
Correct answer: D) Closer to $1$ than to $0.5$.
Which of these descriptions matches a probability of $0.25$?
A) It is unlikely but possible
B) It is almost certain
C) It is certain
D) It is impossible
Correct answer: A) It is unlikely but possible.
Two events $A$ and $B$ have probabilities $P(A)=0.3$ and $P(B)=0.9$. Which event is more likely?
A) Event $A$
B) There is not enough information
C) Event $B$
D) They are equally likely
Correct answer: C) Event $B$.
If an event is described as "almost certain", which probability is most reasonable?
A) $0.01$
B) $0.99$
C) $0.5$
D) $0.2$
Correct answer: B) $0.99$.
A weather forecast gives a $0.8$ probability of rain. How should this be interpreted?
A) Rain is impossible
B) Rain is certain
C) Rain is very likely but not guaranteed
D) Rain is equally likely as not
Correct answer: C) Rain is very likely but not guaranteed.
If $P(A)=0.6$, which of the following is the probability that $A$ does not happen?
A) $0.4$
B) $1.6$
C) $0.6$
D) $-0.4$
Correct answer: A) $0.4$.
A spinner is equally likely to land on any of its coloured sections. If the probability of landing on red is $\dfrac{1}{5}$, what is the probability of not landing on red?
A) $\dfrac{2}{5}$
B) $\dfrac{1}{5}$
C) $\dfrac{4}{5}$
D) $\dfrac{3}{5}$
Correct answer: C) $\dfrac{4}{5}$.
Which statement about the sum of probabilities of all possible outcomes in an experiment is TRUE?
A) The sum is $0$
B) The sum is $1$
C) The sum is $0.5$
D) The sum can be any value
Correct answer: B) The sum is $1$.
On a probability scale, which pair of words best matches the extremes $0$ and $1$?
A) Maybe and definitely not
B) Unlikely and likely
C) Rare and frequent
D) Impossible and certain
Correct answer: D) Impossible and certain.
A student says, "The probability of this event is $1.5$". What is wrong with this statement?
A) Probabilities cannot be less than $2$
B) Probabilities must be negative
C) Probabilities cannot be greater than $1$
D) Probabilities must equal $0.5$
Correct answer: C) Probabilities cannot be greater than $1$.
Which statement about probabilities is TRUE?
A) They are always positive and greater than $1$
B) They must always be written as fractions
C) They are always between $0$ and $1$ inclusive
D) They can be any real number
Correct answer: C) They are always between $0$ and $1$ inclusive.
On the probability scale, which value represents an event that is certain to happen?
A) $\dfrac{1}{4}$
B) $0$
C) $1$
D) $0.5$
Correct answer: C) $1$.
Two fair dice are rolled. What is the probability that the total is $2$?
A) $\dfrac{1}{6}$
B) $\dfrac{1}{12}$
C) $\dfrac{1}{36}$
D) $\dfrac{2}{36}$
Correct answer: C) $\dfrac{1}{36}$.
A bag contains $6$ red and $4$ green counters. One counter is taken at random. What is the probability it is green?
A) $\dfrac{4}{6}$
B) $\dfrac{2}{5}$
C) $\dfrac{3}{5}$
D) $\dfrac{1}{2}$
Correct answer: B) $\dfrac{2}{5}$.
If two events are equally likely, what can be said about their probabilities?
A) Their product is greater than $1$
B) Their sum is $0$
C) One is twice the other
D) They are equal
Correct answer: D) They are equal.
Theoretical probability assumes that
A) only one outcome can occur
B) no outcomes are possible
C) all outcomes in the sample space are equally likely
D) experimental data is always available
Correct answer: C) all outcomes in the sample space are equally likely.
When a fair six-sided die is rolled, what is the theoretical probability of getting a $5$?
A) $\dfrac{5}{6}$
B) $\dfrac{2}{6}$
C) $\dfrac{1}{6}$
D) $\dfrac{1}{5}$
Correct answer: C) $\dfrac{1}{6}$.
A fair coin is tossed twice. How many outcomes are in the sample space?
A) $3$
B) $2$
C) $4$
D) $6$
Correct answer: C) $4$.
A fair coin is tossed once. What is the theoretical probability of getting heads?
A) $\dfrac{1}{4}$
B) $\dfrac{1}{2}$
C) $1$
D) $0$
Correct answer: B) $\dfrac{1}{2}$.
A number is chosen at random from $1$ to $10$. What is the probability that it is even?
A) $\dfrac{2}{5}$
B) $\dfrac{1}{2}$
C) $\dfrac{1}{10}$
D) $\dfrac{3}{10}$
Correct answer: B) $\dfrac{1}{2}$.
The complement of event $A$ is the event that
A) $A$ does not occur
B) $A$ occurs twice
C) both $A$ and $B$ occur
D) $A$ occurs
Correct answer: A) $A$ does not occur.
If events $A$ and $B$ are mutually exclusive, which equation is TRUE?
A) $P(A\text{ or }B) = 0$
B) $P(A\text{ or }B) = P(A)P(B)$
C) $P(A\text{ or }B) = P(A) + P(B)$
D) $P(A\text{ or }B) = P(A) - P(B)$
Correct answer: C) $P(A\text{ or }B) = P(A) + P(B)$.
A bag contains $5$ red counters and $3$ blue counters. One counter is chosen at random. What is the probability of choosing a red counter?
A) $\dfrac{5}{3}$
B) $\dfrac{5}{8}$
C) $\dfrac{1}{5}$
D) $\dfrac{3}{8}$
Correct answer: B) $\dfrac{5}{8}$.
A spinner has $8$ equal sections numbered $1$ to $8$. What is the probability of landing on a number greater than $6$?
A) $\dfrac{1}{4}$
B) $\dfrac{1}{2}$
C) $\dfrac{3}{8}$
D) $\dfrac{1}{8}$
Correct answer: A) $\dfrac{1}{4}$.
A single card is drawn at random from a standard pack of $52$ cards. What is the probability that it is a heart?
A) $\dfrac{4}{13}$
B) $\dfrac{1}{13}$
C) $\dfrac{1}{4}$
D) $\dfrac{13}{52}$
Correct answer: C) $\dfrac{1}{4}$.
An ordinary die is rolled. What is the probability of getting a number less than $5$?
A) $\dfrac{5}{6}$
B) $\dfrac{2}{3}$
C) $\dfrac{1}{3}$
D) $\dfrac{1}{2}$
Correct answer: B) $\dfrac{2}{3}$.
If $P(A)=0.7$, what is $P(A')$?
A) $0.7$
B) $-0.3$
C) $0.3$
D) $1.7$
Correct answer: C) $0.3$.
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