Mathematics for IGCSE & O level - Probability (Section 7)
1
A standard six-sided die is rolled twice. What is the probability of getting a 6 on both rolls?
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(C)
1/36
2
A person has a 60% chance of passing a test. What is the probability of them *failing* the test?
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(B)
40%
3
If the probability of rain is 60% and the probability of wind is 30%, and the events are independent, what is the probability of both rain *and* wind?
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(B)
18%
4
What is the probability of drawing a red card (heart or diamond) from a standard deck of 52 playing cards?
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(B)
1/2
5
What is the probability of not getting a multiple of 3 on a single spin of the spinner described in the previous question?
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(B)
2/3
6
A school has 100 students. 60 students take art, 40 take music, and 20 take both. If a student is selected at random, what is the probability they take *either* art or music?
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(A)
0.8
7
A spinner is divided into 5 equal sections, numbered 1 to 5. What is the probability of spinning an even number?
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(B)
2/5
8
If an event is certain to happen, what is its probability?
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(C)
1
9
What is the relationship between the complement of an event and the event itself?
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C
D
10
What does the probability of an event being 0 represent?
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(B)
The event is impossible.
11
Which of the following describes the meaning of 'relative frequency' in probability?
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(C)
The ratio of the number of times an event occurs to the total number of trials.
12
A fair coin is tossed twice. What is the probability of getting at least one tail?
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(C)
3/4
13
A coin is tossed three times. What is the probability of getting tails all three times?
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(C)
1/8
14
A bag contains 4 red balls and 8 blue balls. What is the probability of choosing a red ball?
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(C)
4/12
15
If the probability of rain tomorrow is 30%, what is the probability it will *not* rain tomorrow?
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(B)
70%
16
A jar contains 8 red balls and 12 blue balls. If you randomly select a ball, what is the probability of choosing a red ball?
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(A)
2/5
17
A spinner is divided into 3 equal sections, colored red, green, and blue. What is the probability of the spinner landing on green?
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(B)
1/3
18
If the odds of a horse winning a race are 1:3, what is the probability of the horse winning?
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(B)
1/4
19
What is the probability of selecting a face card (Jack, Queen, or King) from a standard deck of 52 cards?
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(D)
3/13
20
What is the probability of rolling a number greater than 4 on a standard six-sided die?
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(B)
2/6
21
A box contains 3 blue and 5 red marbles. If one marble is selected at random, what is the probability that it is red?
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(B)
5/8
22
What is the expected frequency of an event?
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(A)
The probability of an event multiplied by the total number of observations of the event.
23
A bag contains 5 red, 7 blue and 3 green marbles. What is the probability that a marble chosen at random is not green?
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(B)
12/15
24
Sarah rolls a fair six-sided die. What is the probability she rolls a number greater than 4?
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(A)
1/6
25
What are dependent events?
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(C)
Events where the outcome of one influences the outcome of the other.
26
If two events are independent, which statement is accurate?
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(C)
The probability of one event is unaffected by the other.
27
If the probability of an event is 0.75, what is the probability of the event *not* occurring?
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(A)
0.25
28
A bag contains 4 red and 6 green marbles. What is the probability of picking a red marble?
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(C)
4/10
29
What is the relationship between the probability of an event occurring and the probability of the event *not* occurring?
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(B)
They add up to 1.
30
What's the probability of the train being late on the first two days, given the probability of a train being late is 0.7?
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(B)
0.49
31
What is relative frequency?
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(C)
The number of times an event occurs divided by the total number of trials.
32
Which of the following events are independent?
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B
C
D
33
What is one key difference between the calculation of independent events to dependent events?
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(A)
The probabilities of the event on the second set of branches are different
34
Which of the following situations represents independent events?
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(B)
Flipping a coin and then rolling a die.
35
What is the probability of drawing a queen from a standard deck of 52 cards?
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(C)
4/52
36
Two dice are rolled. What is the probability of rolling a 6 on one die and a 1 on the other? (Assume the dice rolls are independent)
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(B)
1/12
37
A fair coin is flipped twice. What is the probability of getting at least one head?
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(C)
3/4
38
A bag contains 6 red and 9 blue marbles. What is the probability of picking a red marble?
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(C)
2/5
39
If events A and B are mutually exclusive, what is the probability of either A or B happening? (P(A or B))
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(A)
P(A) + P(B)
40
What's the probability of getting at least one head when tossing a coin twice?
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(C)
3/4
41
If the odds in favor of an event are 3:2, what is the probability of that event occurring?
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(B)
3/5
42
A bag contains 4 red and 4 blue marbles. What is the probability of drawing a blue marble?
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(C)
1/2
43
A spinner has five equal sections numbered 1 to 5. What is the probability of spinning a 3?
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(A)
1/5
44
If a ball is selected at random from a bag containing seven blue and three red balls, and is NOT replaced, what type of event is this?
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(C)
Dependent
45
What is the probability of getting a 2 or a 5 when rolling a single six-sided die?
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(B)
1/3
46
Two dice are rolled. What is the probability the sum of the numbers is 7?
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(C)
5/36
47
If two events, A and B, are independent, and P(A) = 0.3 and P(B) = 0.5, what is P(A and B)?
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(B)
0.15
48
Which of the following statements are true regarding the probability of an event?
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A
B
D
49
In probability theory, what does the term 'independent events' signify?
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(C)
Events whose probabilities are not affected by each other.
50
What is the range of values that a probability can have?
