Find the probability of a couple having a baby boy when their fourth child is born, given that the first three children were all boys. assume boys and girls are equally likely. is the result the same as the probability of getting sall boys among four children

Assuming an independent random process, outcomes are independent of previous outcomes. Dependence may happen (e. g. medical reasons) but then the process is no longer random.

Given independent and random process with equal probability between boys and girls, and that the three previous children are all boys, the probability of a boy as a fourth child remains as 1/2.

However, if the genders of children are unknown, or children are not yet born, then the probability of getting all boys among four children is (1/2) ^4=1/16.

This means that among a large number of random samples of families with four children, approximately 1/16 of them would have four boys.

For more detailed concepts, read up on the law of large numbers, and the definition of probability.