TOPIC：Probability Basics
1 [Maximum mark: 7]
The following Venn diagram shows two events 𝐴 and 𝐵, where P(𝐴) = 0.3, P(𝐴 ∩ 𝐵) = 0.2 and
P(𝐴 ∪ 𝐵) = 0.7. The values of 𝑝, 𝑞, 𝑟 and 𝑠 are probabilities.
(a) Write down the value of 𝑟. [1]
(b) Find the value of:
(i) 𝑝;
(ii) 𝑞;
(iii) 𝑠.
[4]
(c) Find P(𝐵).
[2]
2 [Maximum mark: 5]
A box contains 8 green and 4 blue marbles. Two marbles are selected at random (without
replacement). Find the probability that selected marbles are:
(a) of the same colour; [3]
(b) of different colours. [2]
TOPIC：Probability Basics
3 [Maximum mark: 6]
Two events 𝐴 and 𝐵 are such that P(𝐴) = 0.25 and P(𝐴 ∪ 𝐵) = 0.7.
Find P(𝐵), given that 𝐴 and 𝐵 are:
(a) mutually exclusive; [2]
(b) independent.
[4]
4 [Maximum mark: 5]
𝐴 and 𝐵 are independent events with P(𝐴) = 0.28 and P(𝐴 ∪ 𝐵) = 0.75. Find P(𝐵).
5 [Maximum mark: 6]
The following Venn diagram shows two events 𝐴 and 𝐵, where P(𝐴) = 0.3, P(𝐵) = 0.8 and
P(𝐴 ∩ 𝐵) = 0.2. The values of 𝑝, 𝑞, 𝑟 and 𝑠 are probabilities.
(a) Find the value of 𝑟, 𝑝, 𝑞, and 𝑠. [4]
(b) Find P(𝐴 ∣ 𝐵′ ). [2]
TOPIC：Probability Basics
6 [Maximum mark: 6]
Two events 𝐴 and 𝐵 are such that P(𝐴′ ∩ 𝐵) = P(𝐴 ∩ 𝐵′ ) = 0.3 and P(𝐴 ∩ 𝐵) = 0.2.
(a) Calculate P(𝐴′ ∩ 𝐵′ ).[2]
(b) Calculate P(𝐵′ ).[2]
(c) Hence find P(𝐴′ ∣ 𝐵′ ). [2]
7 [Maximum mark: 15]
Bag 𝐴 contains 4 red balls and 3 green balls. Bag 𝐵 contains 4 red balls and 1 green ball.
(a) A ball is randomly chosen from both bags. Find the probability they are of different
colours. [4]
A bias coin is flipped. If heads is shown, a ball is randomly selected from bag 𝐴. If tails is
shown, a ball is randomly selected from bag 𝐵.
(b) Complete the tree diagram below. [4]
(c) The bias coin is flipped and a ball is randomly selected. Find the probability the ball is
red. [4]
(d) Given that a red ball is selected, find the probability the bias coin showed heads. [3]
TOPIC：Probability Basics
8 [Maximum mark: 11]
Jack and John decided to run a total of 250 km in 31 days. To help them decide whether it is
fine to go running, they classify each day in August as rainy or dry. Given that a day in
August is rainy, the probability that the next day is dry is 0.25. Given that a day in August
is dry, the probability that the next day is dry is 0.8. The weather forecast for the 1 st of
August predicts that the probability that it will be dry is 0.9.
(a) Draw a tree diagram to display all the possible outcomes for the first three days of August.
[4]
(b) Find the probability that the 3rd of August is dry.
[3]
(c) Find the probability that the 1st of August was dry given that the 3rd of August is rainy.
[4]