1.
A fair six-sided dice is rolled. Find P(even number). [1]
JD SCIENCE
Probability
Answer all questions. Show working. Answers are in a separate file on the Worksheets page — do not look at them until you have finished.
2.
Two fair coins are flipped. Find P(two heads). [2]
3.
A bag contains 8 red and 10 blue counters. One counter is taken at random. Find P(red). [2]
4.
A spinner has sections A, A, B, C. It is fair.
(a) Find P(A). [1]
(b) The spinner is spun twice. Find P(A then B). [2]
5.
P(rain) = 0.3. Find P(not rain). [1]
6.
Events A and B are mutually exclusive. P(A) = 0.2, P(B) = 0.5. Find P(A or B). [2]
7.
Events C and D are independent. P(C) = 0.4, P(D) = 0.5. Find P(C and D). [2]
8.
A bag has 3 red and 5 green sweets. Two sweets are taken without replacement. Find P(both red). [3]
9.
Using the same bag, find P(one of each colour) when two sweets are taken without replacement. [4]
10.
Draw a complete tree diagram for two flips of a biased coin with P(H) = 0.6. Label all eight probabilities on the branches and ends. [4]
11.
A two-way table: 20 students, 12 study French, 9 study German, 5 study both. How many study neither? [3]
12.
From that table, a student is chosen at random. Find P(studies French | studies German). [3]
13.
Write the formula for P(A|B) and explain it in words. [2]
14.
The probability of winning a game is 0.15. The game is played 200 times. Estimate the number of wins. [2]
15.
Relative frequency of a 6 after 50 rolls is 0.1. After 500 rolls it is 0.16. Which is the better estimate of P(6) on a fair dice, and why? [3]
16.
A letter is chosen from MISSISSIPPI. Find P(S). [2]
17.
Two events: P(A) = 0.3, P(B) = 0.4, P(A and B) = 0.12. Are A and B independent? Show working. [3]
18.
P(A) = 0.6, P(B) = 0.5, P(A and B) = 0.2. Find P(A or B). [2]
19.
What is a sample space? List the sample space when a coin is flipped and a dice is rolled. [3]
20.
A fair spinner 1–5 is spun twice. Find P(sum is 10). [2]
21.
Find P(sum is 6) for two fair dice. [3]
22.
Explain the difference between independent events and mutually exclusive events. Give an example of each. [4]
23.
Owain picks a number from 1 to 20. Find P(prime). [2]
24.
A Venn diagram has P(A) = 0.5, P(B) = 0.4 and P(A and B) = 0.15.
(a) Find P(only A). [2]
(b) Find P(neither). [2]
25.
Without replacement: 10 tickets numbered 1–10. Two tickets are drawn. Find P(both even). [3]
26.
Why must probabilities on a set of mutually exclusive exhaustive outcomes add up to 1? [2]
27.
A biased dice has P(6) = 0.3. It is rolled twice. Find P(at least one 6). [3]
28.
Expected winnings: a game costs £2. P(win £10) = 0.1, otherwise win nothing. Is the game fair? Show working. [3]
29.
Describe how to use a set of random numbers from 00 to 99 to simulate P(success) = 0.27. [2]
30.
A WJEC tree-diagram question is often 4 marks. State what must be labelled on the branches and on the ends. [2]
31.
Three fair coins. Find P(exactly two heads). [3]
32.
The probability of an event is 0. Explain what this means. The probability is 1. Explain what this means. [2]