Worksheet Chapter 9: Probability of Combined Events

1. A box contains 4 red cards and 6 blue cards. Two cards are chosen at random ONE BY ONE WITHOUT REPLACEMENT. (a) Draw or describe the tree diagram branches for this scenario. (b) Calculate the probability that both cards drawn are of the SAME color. (c) Calculate the probability that at least one card is red.

2. True or False: Selecting two students one after another without replacement from a group of 20 represents dependent events.

3. True or False: If two events are mutually exclusive, then P(A ∩ B) = P(A) × P(B).

4. Which of the following expressions represents the probability of the complement of event (A ∪ B)?

5. A fair dice with faces numbered 1 to 6 is rolled once. Let Event A be obtaining an odd number and Event B be obtaining a prime number. (a) List the elements of Event A and Event B. (b) State whether Event A and Event B are mutually exclusive. Justify your answer. (c) Calculate P(A ∪ B).

6. A drawer contains 4 black socks and 6 white socks. A sock is drawn at random and replaced before drawing a second sock. Calculate the probability of drawing two black socks in succession.

7. Two archers, Sarah and Mei Ling, shoot at a target independently. The probability that Sarah hits the target is 34 and the probability that Mei Ling hits the target is 23. (a) Construct a probability tree diagram or branch list showing all possible combined outcomes. (b) Calculate the probability that ONLY ONE archer hits the target. (c) Calculate the probability that the target is hit (at least one archer hits).

8. Box X contains 3 red balls and 2 yellow balls. Box Y contains 1 red ball and 4 yellow balls. A ball is transferred at random from Box X into Box Y, and then a ball is drawn at random from Box Y. (a) Find the probability that the ball transferred from Box X is red. (b) Calculate the total probability that the ball drawn from Box Y is RED.

9. Fill in the blank: Two events A and B are ________ if the occurrence of event A does not affect the probability of event B occurring.

10. In a sports club, the probability that a member plays badminton is 0.6, the probability that a member plays tennis is 0.5, and the probability that a member plays both badminton and tennis is 0.3. (a) Calculate the probability that a randomly chosen member plays badminton OR tennis. (b) Calculate the probability that a member plays NEITHER badminton NOR tennis.