James and Catherine are a married couple. They have two children, one of
the child is a boy. Assume that the probability of each gender is 1/2.
What is the probability that the other child is also a boy?
What is the probability that the other child is also a boy?
The probability is the same as the first time. It is like a coin toss. History plays no role. The probability is 1/2. If we did not know that the first child is a boy, the probability of having two boys would be 1/4.
ReplyDeleteThey have two children. The probabilities are:
ReplyDeleteP(BB) = 1/4
P(BG) = 1/4
P(GB) = 1/4
P(GG) = 1/4
One of the children is a boy, so we can eliminate the GG option. This leaves us with the first three scenarios still as viable options. Of the three options remaining, only 1 of the 3 options is BB. Thus, the probability is 1/3.
Saying "one of the children is a boy" is different than the case where they said something like "The older child is a boy." In that case it would be 1/2, not 1/3.
1/2. Mutually exclusive events.
ReplyDeleteA thorough description is here:
ReplyDeletehttps://en.wikipedia.org/wiki/Boy_or_Girl_paradox
Josh, you answered the question "What is the probability that both children are boys?"
ReplyDeleteThis riddle is:
"What is the probability that the other child is also a boy?"
1/3
ReplyDelete