Mathematics for IGCSE & O level - Probability (Section 6)
1
There are 6 red balls and 4 blue balls. What is the probability of selecting two red balls without replacement?
Απάντηση
(A)
9/25
2
A committee of 3 people is to be selected from a group of 5 men and 7 women. If the selection is random, and the events of selecting each person are considered independent, what is the probability of selecting 3 women?
Απάντηση
(A)
(7/12) * (6/11) * (5/10)
3
A weather forecast states a 20% chance of rain. What are the odds against rain (in fractional form)?
Απάντηση
(D)
4/1
4
A weather forecast predicts a 40% chance of rain. What is the probability that it will *not* rain?
Απάντηση
(C)
60%
5
Which of the following events are mutually exclusive?
Απάντηση
A
B
D
6
If the odds of a team winning a game are 2:5, what is the probability that the team *loses* the game?
Απάντηση
(B)
5/7
7
If the probability of an event occurring is 0.4, what is the probability of the event not occurring?
Απάντηση
(C)
0.6
8
Which of the following best defines a sample space?
Απάντηση
(C)
The set of all possible outcomes of an experiment.
9
A bag contains 5 red marbles and 7 blue marbles. What is the probability of selecting a red marble?
Απάντηση
(C)
5/12
10
What is the probability of rolling an even number on a standard six-sided die?
Απάντηση
(C)
1/2
11
A bag contains 5 red and 5 blue marbles. What is the probability of selecting a red marble *or* a blue marble?
Απάντηση
(D)
1
12
Which of the following scenarios describes independent events?
Απάντηση
(B)
Flipping a coin and rolling a six-sided die.
13
Which of the following events are mutually exclusive?
Απάντηση
A
D
14
In probability, what does the term 'event' refer to?
Απάντηση
(A)
A set of one or more outcomes.
15
Two dice are rolled. What is the probability that the sum of the numbers is 10?
Απάντηση
(B)
1/12
16
What are the main characteristics of independent events?
Απάντηση
(B)
The outcome of one event does not affect the outcome of the other.
17
If the probability of an event occurring is 2/3, what is the probability of that event *not* occurring?
Απάντηση
(A)
1/3
18
What is a key difference in a tree diagram between independent and dependent events?
Απάντηση
(B)
The probabilities on the second set of branches are different.
19
When are two events considered mutually exclusive?
Απάντηση
(B)
When they cannot both occur at the same time.
20
What is the probability of drawing an ace from a standard deck of 52 playing cards?
Απάντηση
(B)
4/52
21
Two six-sided dice are rolled. What is the probability the sum of the two dice is 1?
Απάντηση
(A)
0
22
What is the relationship between probability and relative frequency?
Απάντηση
(B)
Relative frequency is an estimate of probability.
23
A fair coin is flipped once. What is the probability of getting heads?
Απάντηση
(C)
1/2
24
A bag contains 5 red marbles and 3 blue marbles. What is the probability of selecting a red marble, replacing it, and then selecting a blue marble?
Απάντηση
(A)
15/64
25
If the probability of it raining is 0.3, what is the probability that it does not rain?
Απάντηση
(B)
0.7
26
If the probability of an event is 0.7, what are the odds *against* that event happening?
Απάντηση
(B)
3:7
27
What is the probability of getting tails when you flip a fair coin?
Απάντηση
(C)
1/2
28
A fair six-sided die is rolled. What is the probability of rolling a number less than 3?
Απάντηση
(B)
2/6
29
If a train arrives on time with a probability of 0.7, what's the probability the train will be late on three consecutive days?
Απάντηση
(C)
0.027
30
A spinner has 4 equal sections: red, blue, green, and yellow. What is the probability the spinner lands on red or yellow?
Απάντηση
(B)
1/2
31
What is the fundamental principle behind calculating the probability of independent events?
Απάντηση
(C)
Multiplying the individual probabilities.
32
If the probability that Gary and Rashna were both born on a Monday is equal likelihood. What is the probability?
Απάντηση
(B)
1/49
33
What is a characteristic of independent events?
Απάντηση
(B)
The outcome of one has no impact on the probability of the other.
34
Which of the following statements about probabilities are true?
Απάντηση
B
C
D
35
Two dice are rolled. What is the probability the sum of the numbers is an even number?
Απάντηση
(B)
1/2
36
A bag contains 3 red marbles, 4 blue marbles, and 2 green marbles. What is the probability of randomly selecting a blue marble?
Απάντηση
(B)
4/9
37
If the probability of an event happening is 0.2, what is the probability of that event *not* happening?
Απάντηση
(C)
0.8
38
In a survey of 100 people, 60 like cats and 30 like dogs. If liking cats and dogs is independent, what is the probability a person likes both cats and dogs?
Απάντηση
(B)
0.18
39
A die is rolled. What is the probability of rolling a number greater than 2?
Απάντηση
(D)
2/3
40
If the probability of winning a lottery is 1/1,000,000, what does this mean?
Απάντηση
(C)
You have a very small chance of winning.
41
What is the key difference between independent and dependent events in terms of calculating probabilities?
Απάντηση
(D)
The probabilities on the second set of branches in a tree diagram are the same for independent events and different for dependent events.
42
What are the different ways to express the probability of an event?
Απάντηση
A
B
D
43
Which of the following statements are true regarding probabilities?
Απάντηση
A
B
C
44
What is the range of possible values for any probability?
Απάντηση
B
C
45
If the probability of Event A is 0.6 and the probability of Event B is 0.4, and the events are independent, what is the probability of A happening and B not happening?
Απάντηση
(B)
0.36
46
If the probability of an event occurring is 3/5, what is the probability that the event will *not* occur?
Απάντηση
(A)
2/5
47
A spinner has 8 equal sections numbered 1 through 8. What is the probability of spinning an odd number?
Απάντηση
(B)
1/2
48
A die is rolled. What is the probability of getting a number less than or equal to 2?
Απάντηση
(B)
2/6
49
Which of the following events are *dependent*?
Απάντηση
A
C
50
Two dice are rolled. What is the probability of rolling a double (both dice show the same number)?
