A bag contains 10 red balls and 3 black balls. Siyabonga picks a ball at random from the bag and replaces it back in the bag. He mixes the balls in the bag and then picks another ball at random from the bag. What is the probability of choosing a red ball and a black ball from the bag? TIP: You need to construct a tree diagram and use it to calculate the probability for this event. INSTRUCTION: Your answer must be a fraction in its lowest terms. Answer: The probability of choosing a red ball and a black ball from the bag is

To find the probability of choosing a red ball and a black ball from the bag, we can first outline the possible outcomes using a tree diagram. The first pick can either be a red (R) or a black (B) ball. 1. If the first ball picked is red (with a probability of 10/13), the second pick can again be red or black. - If the second pick is red: (10/13) * (10/13) = 100/169. - If the second pick is black: (10/13) * (3/13) = 30/169. 2. If the first ball picked is black (with a probability of 3/13), the second pick can again be red or black. - If the second pick is red: (3/13) * (10/13) = 30/169. - If the second pick is black: (3/13) * (3/13) = 9/169. Now, we want the probability of getting one red and one black ball in any order: - Probability of red first and black second: 30/169 - Probability of black first and red second: 30/169 Adding these probabilities gives us: 30/169 + 30/169 = 60/169. Thus, the probability of choosing a red ball and a black ball from the bag is **60/169**.