Question

What are the chances that a family with three children has only sons? After two sons, what is the probability that the next child will be a boy?

Answer 1

The chances of a family with three children having only sons is 0.125 or 12.5%. After having two sons, the probability of the next child being a boy remains the same, which is 0.5 or 50%.

Step-by-step explanation:

The chances of a family with three children having only sons can be determined using the concept of probability. Each child has a 50% chance of being a boy or a girl, assuming an equal probability for each gender. So the probability of having only sons is calculated as:

Probability of having only sons = (Probability of first child being a son) x (Probability of second child being a son) x (Probability of third child being a son) = 0.5 x 0.5 x 0.5 = 0.125

So, the chances of a family with three children having only sons is 0.125 or 12.5%.

After having two sons, the probability of the next child being a boy remains the same, which is 0.5 or 50%.