Let’s visit our favourite subject, but after a long gap – the probability and Bayes’ theorem. Here is the question:
A new child arrives in a child-care facility that has three boys and the remaining girls. A statistician visits the centre and randomly picks up a boy child. What is the chance that the newly admitted child is a boy?
Before solving the puzzle, let the number of girls already in the centre be g. Therefore, the total number of children available for the statistician to count is 3 + 1 + g = 4 + g.
The Bayes’ equation is
The terms are
P(B_n | B_r) = probability of the new child being a boy given the randomly picked is a boy
P(B_r | B_n) = probability of picking a random boy given the new child is a boy = 4 /(4+g)
P(B_r | G_n) = probability of picking a random boy given the new child is a girl = 3/ (4+g)
P(B_n) = prior probability for the new child to be a boy = 0.5
P(G_n) = prior probability for the new child to be a girl = 0.5
Substituting the terms,
