Drawing Balls Probability

00:00 7 marks

A bag contains 5 red balls and 7 blue balls. Two balls are drawn from the bag without replacement.

(a) Draw a tree diagram to represent this situation, showing the probabilities on the branches. [3]
(b) Find the probability that both balls drawn are blue. [2]
(c) Find the probability that the second ball drawn is red, given that the first ball drawn was blue. [2]

Hint Hint

Hint

For part (a), make sure to indicate the probabilities for red and blue on the first draw and adjust them accordingly for the second draw. For part (c), use the fact that after drawing a blue ball, the remaining red balls and total balls change.

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Answer Answer

Complete Answer

a) The tree diagram must have a first branch with red (5/12) and blue (7/12) outcomes. For the red branch, the second draw gives red with probability 4/11 and blue with 7/11; for the blue branch, it gives red with probability 5/11 and blue with 6/11. b) The probability that both balls are blue is (7/12) × (6/11) = 42/132 = 7/22 (approximately 0.318). c) Given that the first ball is blue, the probability that the second ball is red is 5/11 (approximately 0.455).

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