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?
Answer
(C)
1/36
2
A person has a 60% chance of passing a test. What is the probability of them *failing* the test?
Answer
(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?
Answer
(B)
18%
4
What is the probability of drawing a red card (heart or diamond) from a standard deck of 52 playing cards?
Answer
(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?
Answer
(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?
Answer
(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?
Answer
(B)
2/5
8
If an event is certain to happen, what is its probability?
Answer
(C)
1
9
What is the relationship between the complement of an event and the event itself?
Answer
C
D
10
What does the probability of an event being 0 represent?
Answer
(B)
The event is impossible.
11
Which of the following describes the meaning of 'relative frequency' in probability?
Answer
(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?
Answer
(C)
3/4
13
A coin is tossed three times. What is the probability of getting tails all three times?
Answer
(C)
1/8
14
A bag contains 4 red balls and 8 blue balls. What is the probability of choosing a red ball?
Answer
(C)
4/12
15
If the probability of rain tomorrow is 30%, what is the probability it will *not* rain tomorrow?
Answer
(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?
Answer
(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?
Answer
(B)
1/3
18
If the odds of a horse winning a race are 1:3, what is the probability of the horse winning?
Answer
(B)
1/4
19
What is the probability of selecting a face card (Jack, Queen, or King) from a standard deck of 52 cards?
Answer
(D)
3/13
20
What is the probability of rolling a number greater than 4 on a standard six-sided die?
Answer
(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?
Answer
(B)
5/8
22
What is the expected frequency of an event?
Answer
(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?
Answer
(B)
12/15
24
Sarah rolls a fair six-sided die. What is the probability she rolls a number greater than 4?
Answer
(A)
1/6
25
What are dependent events?
Answer
(C)
Events where the outcome of one influences the outcome of the other.
26
If two events are independent, which statement is accurate?
Answer
(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?
Answer
(A)
0.25
28
A bag contains 4 red and 6 green marbles. What is the probability of picking a red marble?
Answer
(C)
4/10
29
What is the relationship between the probability of an event occurring and the probability of the event *not* occurring?
Answer
(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?
Answer
(B)
0.49
31
What is relative frequency?
Answer
(C)
The number of times an event occurs divided by the total number of trials.
32
Which of the following events are independent?
Answer
B
C
D
33
What is one key difference between the calculation of independent events to dependent events?
Answer
(A)
The probabilities of the event on the second set of branches are different
34
Which of the following situations represents independent events?
Answer
(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?
Answer
(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)
Answer
(B)
1/12
37
A fair coin is flipped twice. What is the probability of getting at least one head?
Answer
(C)
3/4
38
A bag contains 6 red and 9 blue marbles. What is the probability of picking a red marble?
Answer
(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))
Answer
(A)
P(A) + P(B)
40
What's the probability of getting at least one head when tossing a coin twice?
Answer
(C)
3/4
41
If the odds in favor of an event are 3:2, what is the probability of that event occurring?
Answer
(B)
3/5
42
A bag contains 4 red and 4 blue marbles. What is the probability of drawing a blue marble?
Answer
(C)
1/2
43
A spinner has five equal sections numbered 1 to 5. What is the probability of spinning a 3?
Answer
(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?
Answer
(C)
Dependent
45
What is the probability of getting a 2 or a 5 when rolling a single six-sided die?
Answer
(B)
1/3
46
Two dice are rolled. What is the probability the sum of the numbers is 7?
Answer
(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)?
Answer
(B)
0.15
48
Which of the following statements are true regarding the probability of an event?
Answer
A
B
D
49
In probability theory, what does the term 'independent events' signify?
Answer
(C)
Events whose probabilities are not affected by each other.
50
What is the range of values that a probability can have?
