Three young children approach a gum ball machine, each with a nickel to spend. The machine has just been filled with 50 black, 150 white, 100 red and 100 yellow balls that have been thoroughly mixed. Sue and Jim approached the machine first. They both said they wanted red gum balls. What is the likelihood they both will get their wish?
Click on the arrows to vote for the correct answer
A. B. C. D. E.Explanation
100/400*99/399 = 0.062
To solve this problem, we need to calculate the probability of both Sue and Jim selecting red gum balls from the machine.
Let's break down the problem step by step:
Step 1: Calculate the probability of Sue selecting a red gum ball. The total number of gum balls in the machine is 50 black + 150 white + 100 red + 100 yellow = 400. The number of red gum balls is 100. Therefore, the probability of Sue selecting a red gum ball is 100/400 = 0.25.
Step 2: Calculate the probability of Jim selecting a red gum ball. After Sue selects a gum ball, the number of red gum balls remaining in the machine is 100 - 1 = 99. The total number of gum balls remaining in the machine is 400 - 1 = 399. Therefore, the probability of Jim selecting a red gum ball is 99/399 ≈ 0.248.
Step 3: Calculate the joint probability of both Sue and Jim selecting red gum balls. To calculate the joint probability, we multiply the individual probabilities together: P(Sue and Jim selecting red gum balls) = P(Sue selects red) * P(Jim selects red) ≈ 0.25 * 0.248 = 0.062.
Therefore, the likelihood that both Sue and Jim will get their wish of selecting red gum balls is approximately 0.062.
The correct answer is B. 0.062.