TOPICοΌProbability Basics 1 [Maximum mark: 7] The following Venn diagram shows two events π΄ and π΅, where P(π΄) = 0.3, P(π΄ ∩ π΅) = 0.2 and P(π΄ ∪ π΅) = 0.7. The values of π, π, π and π are probabilities. (a) Write down the value of π. [1] (b) Find the value of: (i) π; (ii) π; (iii) π . [4] (c) Find P(π΅). [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] TOPICοΌProbability Basics 3 [Maximum mark: 6] Two events π΄ and π΅ are such that P(π΄) = 0.25 and P(π΄ ∪ π΅) = 0.7. Find P(π΅), given that π΄ and π΅ are: (a) mutually exclusive; [2] (b) independent. [4] 4 [Maximum mark: 5] π΄ and π΅ are independent events with P(π΄) = 0.28 and P(π΄ ∪ π΅) = 0.75. Find P(π΅). 5 [Maximum mark: 6] The following Venn diagram shows two events π΄ and π΅, where P(π΄) = 0.3, P(π΅) = 0.8 and P(π΄ ∩ π΅) = 0.2. The values of π, π, π and π are probabilities. (a) Find the value of π, π, π, and π . [4] (b) Find P(π΄ β£ π΅′ ). [2] TOPICοΌProbability Basics 6 [Maximum mark: 6] Two events π΄ and π΅ are such that P(π΄′ ∩ π΅) = P(π΄ ∩ π΅′ ) = 0.3 and P(π΄ ∩ π΅) = 0.2. (a) Calculate P(π΄′ ∩ π΅′ ).[2] (b) Calculate P(π΅′ ).[2] (c) Hence find P(π΄′ β£ π΅′ ). [2] 7 [Maximum mark: 15] Bag π΄ contains 4 red balls and 3 green balls. Bag π΅ 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 π΄. If tails is shown, a ball is randomly selected from bag π΅. (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] TOPICοΌProbability 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]