1/2.
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Assuming the probability of a boy is 0.5, the probability of a boy and boy and boy is 0.5 * 0.5 * 0.5 = 0.125.
The probability is indeterminate. I might ask a student or I might not.
The answer to this is 1 minus the probability that they will have 3 or fewer children. This would happen only if they had a boy as the first, second or third child. The probability they have a boy as first child is 0.5 The probability they have a boy as second is 0.25 The probability they have a boy as third is 0.125 Thus the total probability is 0.875 And so the probability they will have more than three children is 1-0.875 or 0.125
The probability of a boy is still 0.5 no matter how many prior children there are.
Probability of picking a student is 800 / (800+50+150) = 800 / 1000 = .8.