Question

As- sume that the box contains 10 balls: 4 red, 5 blue, and 1 yellow. As in the text, you draw one ball, note its color, and if it is yel- low replace it. If it is not yellow you do not replace it. You then draw a second ball and note its color.

(1) What is the probability that the second ball drawn is yel low?

(2) What is the probability that the second ball drawn is red?

Answer 1

Probability = Favorable outcomes / Total Outcomes

(1) P(second ball drawn is yellow)

We break it into 2 events

Event 1: 1st Ball yellow, replace it and get second ball yellow = (1/10) * (1/10) = 1/100

Event 2: 1st Ball not yellow, don't replace and second ball yellow = (9/10) * (1/9) = 1/10

Therefore the required probability = (1/100) + (1/10) = 11/100 = 0.11

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(2) P(second ball drawn is Red)

We break it into 3 events

Event 1: 1st Ball yellow, replace it and get second ball Red = (1/10) * (4/10) = 4/100

Event 2: 1st Ball Red, don't replace and second ball Red = (4/10) * (3/9) = 12/90

Event 3: 1st Ball Blue, don't replace and second ball Red = (5/10) * (4/9) = 20/90

Therefore the required probability = (4/100) + (12/90) + (20/90) = (36 + 120 + 200) / 900 = 356 / 900 = 89 / 225 = 0.3955

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