A pot contains 5 white and 3 red balls while another pot contains 4 white and 6 red balls. One pot is chosen at random and a ball is drawn from it. If the ball is white, what is the probability that it is from the first pot?
The probability of choosing one pot = 1/2
The probability of choosing white ball in first pot = 1/2 × [ 5C1 / 8C1] = 5/16
The probability of choosing white ball
= 1/2 × [5C1 / 8C1] + 1/2 × [4C1 / 10C1]
= 1/2 × [5/8] + 1/2 × [4/10]
= 5/16 + 1/5 = 41/80 ∴ The probability that it is from the first pot = (5/16) / (41/80)
= 5/16 × 80/41 = 25/41
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