Recent studies suggest that 12 % of the world population is left handed. Depending on parents' hand usage, the chances of having left handed children are as follows: A: Both parents are left handed, chances of having left handed children = 24 % B: Both parents are right handed, chances of having left handed children = 9 % C: Father left handed and mother right handed, chances of having left handed children = 17 % D:

Step-by-step solution

Let L be the event that the child is left-handed. From the given data, the conditional probabilities of having a left-handed child are: P(L A) = 24 100 P(L B) = 9 100 P(L C) = 17 100 P(L D) = 22 100 We are given the prior probabilities: P(A) = P(B) = P(C) = P(D) = 1 4 We need to find the probability that both parents are left-handed given that the child is left-handed, which is P(A L) . Using Bayes' theorem: P(A L) = P(A)P(L A) P(A)P(L A) + P(B)P(L B) + P(C)P(L C) + P(D)P(L D) Substituting the values: P(A L) = 1 4