Question
A bag contains 7 green balls, 5 blue balls, and 10
yellow balls. A box contains 3 green balls and 8 yellow balls. A ball is randomly drawn from the box and put into the bag, and then a ball is randomly drawn from the bag. Find the probability that the ball is of yellow color.Solution
ATQ, Bag: 22 balls (10 yellow). Box: 11 balls (8 yellow, 3 green). Case 1: A yellow ball is added to the bag. Probability of drawing yellow from the box: 8/11. Bag ha 11 yellow out of 23 balls: 11/23. Contribution: 8/11, 11/23 = 88/253.
Case 2: A green ball is added to the bag. Probability of drawing green from the box: 3/11 Bag has 10 yellow out of 23 balls = 10/23 Contribution: 3/11, 10/23 = 30/253 .
Total Probability:
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