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