Mathematics for IGCSE & O level - Probability (Section 5)
1
A die is rolled twice. Which of the following outcomes are possible?
Answer
A
C
2
A fair die is rolled. What is the probability of rolling a number greater than 4 or an even number?
Answer
(C)
2/3
3
Basma picks two pens at random. The bag contains 3 red pens and 5 blue pens. Which is the correct way to find the probability that Basma picks at least one blue pen?
Answer
A
B
C
4
Which of the following represents a mutually exclusive event when rolling a standard six-sided die?
Answer
(A)
Rolling an even number and rolling a 3.
5
If two events are independent, and the probability of Event A is 0.2 and the probability of Event B is 0.4, what is the probability of both events occurring?
Answer
(A)
0.08
6
What does the law of large numbers state?
Answer
(A)
As the number of trials increases, the experimental probability approaches the theoretical probability.
7
If events A and B are mutually exclusive, what is P(A or B) equal to?
Answer
(A)
P(A) + P(B)
8
What is the probability of drawing the Ace of Spades from a standard deck of 52 cards?
Answer
(C)
1/52
9
What is the probability of rolling an even number on a standard six-sided die?
Answer
(C)
1/2
10
A spinner is divided into four equal sections: red, blue, green, and yellow. What is the probability of *not* landing on yellow?
Answer
(C)
3/4
11
A bag contains 3 red, 4 yellow, and 2 green marbles. What is the probability of selecting a red or yellow marble?
Answer
(C)
4/9
12
A bag contains 5 red, 4 blue, and 3 green marbles. What is the probability of selecting a marble that is NOT blue?
Answer
(D)
7/12
13
What does a probability of 0 mean?
Answer
(C)
The event will never happen.
14
What is the probability of getting two heads in a row by tossing a fair coin twice?
Answer
(B)
1/4
15
Two events A and B are independent. P(A) = 0.4, P(B) = 0.3. What is the probability of either A or B occurring?
Answer
(B)
0.58
16
If two events, A and B, are mutually exclusive, and the probability of A is 0.2 and the probability of B is 0.3, what is the probability of A or B happening?
Answer
(B)
0.5
17
A coin is flipped twice. What is the probability of getting two heads?
Answer
(B)
1/4
18
Which is the correct way to express probability?
Answer
(D)
As a decimal, fraction, or percentage between 0 and 100%.
19
What is the probability of choosing a specific card from a standard deck of 52 playing cards?
Answer
A
B
20
When tossing a fair coin twice, what is the probability of getting heads on both tosses?
Answer
(B)
1/4
21
In a probability experiment, what does the term 'sample space' refer to?
Answer
(B)
The set of all possible outcomes.
22
In probability, what does the term 'outcome' refer to?
Answer
(B)
A possible result of an experiment.
23
A bag contains 2 red marbles, 5 blue marbles, and 3 yellow marbles. What is the probability of selecting a blue marble?
Answer
(B)
5/10
24
A die is rolled. What is the probability of getting a 1?
Answer
(B)
1/6
25
If two events, A and B, are independent, how do you calculate the probability of both A and B occurring?
Answer
(C)
P(A) * P(B)
26
What does it mean when the probability of an event is described as 'certain'?
Answer
A
C
27
There are 7 red and 3 yellow balls in a bag. Lee chooses a ball at random, notes its colour and replaces it. What is the probability that Lee chooses a red ball and then a yellow ball?
Answer
(A)
21/100
28
A survey showed that 40% of people prefer coffee and 60% prefer tea. If a person is selected at random, what is the probability they prefer either coffee or tea?
Answer
(D)
100%
29
A spinner has 8 equal sections, numbered 1 to 8. What is the probability of the spinner landing on a number greater than 6?
Answer
(B)
2/8
30
When drawing a ball from the bag. If the first ball selected is not replaced. What will this effect?
Answer
(C)
The probabilities on the second set of branches
31
A card is drawn from a standard deck of 52 cards. What is the probability of drawing a queen or a king?
Answer
(B)
2/13
32
Which events are mutually exclusive?
Answer
A
C
D
33
If the probability of an event happening is 60%, what is the probability of it *not* happening?
Answer
(C)
40%
34
A coin is flipped twice. What is the probability of getting heads both times?
Answer
(B)
1/4
35
A box contains 4 red and 6 blue balls. Two balls are drawn at random without replacement. What is the probability that both balls are red?
Answer
(D)
4/15
36
If an event is impossible, what is its probability?
Answer
(A)
0
37
In a tree diagram, if there are two branches coming from a point, what is the sum of the probabilities on those branches?
Answer
(C)
1
38
If an event is certain to occur, what is its probability?
Answer
(C)
1
39
Which of the following events are independent events?
Answer
A
C
D
40
If two events are independent, what does that mean regarding their probabilities?
Answer
(B)
The probability of one does not affect the probability of the other.
41
A coin is tossed once. What is the probability of getting tails?
Answer
(C)
1/2
42
If there are 5 blue pens and 5 red pens, what is the probability of Basma picking a blue pen? (Basma picks one pen).
Answer
(C)
1/2
43
If the odds of a certain event occurring are 4:1, what is the probability of that event occurring?
Answer
(B)
4/5
44
What does the sample space diagram helps to visualise?
Answer
(B)
The outcomes of two separate events.
45
A weather forecaster says there is a 70% chance of rain. What are the odds of it *not* raining (in fractional form)?
Answer
(B)
3/10
46
A box contains 3 green and 7 yellow marbles. What is the probability of selecting a yellow marble?
Answer
(B)
7/10
47
What is the probability of rolling an even number or a 1 on a standard six-sided die?
Answer
(D)
5/6
48
What is the probability of selecting a diamond from a standard deck of 52 playing cards?
Answer
(C)
1/4
49
If the chance of winning a certain game is 40%, what is the chance of *not* winning the game?
Answer
(C)
60%
50
If the probability of a train arriving on time is 0.7. What is the probability it arrives on time for two out of three days?
