There are one white ball and one black ball in a bag and we take a ball randomly at a time. If it is a white ball, we put three white balls back into the bag, until we get the black ball. What is the probability that we don’t get the black ball by two draws?
Question
There are one white ball and one black ball in a bag and we take a ball randomly at a time. If it is a white ball, we put three white balls back into the bag, until we get the black ball. What is the probability that we don’t get the black ball by two draws?
Solution
For the first draw, there are two balls in the bag, one white and one black. So the probability of drawing a white ball is 1/2.
If we draw a white ball, we put three white balls back into the bag. So for the second draw, there are four balls in the bag, three white and one black. So the probability of drawing a white ball again is 3/4.
Since these are independent events, the probability of both events occurring is the product of their individual probabilities.
So, the probability that we don’t get the black ball by two draws is (1/2) * (3/4) = 3/8 = 0.375.
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