Myrza has three children

a.If his oldest child is a girl, what is the probability that all the children are girls ?

b.Given at least one of them is a boy, what is the probability of all of them are boys ?

To find the probabilities in these scenarios, we can use the concept of conditional probability. Conditional probability calculates the probability of an event occurring given that another event has already occurred.

a. If Myrza's oldest child is a girl, there are two possibilities for the gender of the other two children - both girls or one girl and one boy. However, since we are only interested in the probability that all three children are girls, we can ignore the case of one girl and one boy.

Since the gender of each child is independent of the others, the probability of each child being a girl is 1/2. Therefore, the probability of all three children being girls is (1/2) * (1/2) * (1/2) = 1/8.

So, if Myrza's oldest child is a girl, the probability that all the children are girls is 1/8.

b. If we know that at least one of the children is a boy, there are two possibilities for the genders of the other two children - all boys or two boys and one girl. Here, we are interested in the probability that all three children are boys.

Again, since the gender of each child is independent, the probability of each child being a boy is also 1/2. Therefore, the probability of all three children being boys is (1/2) * (1/2) * (1/2) = 1/8.

However, we have to take into account the condition that at least one of the children is a boy. This condition rules out the possibility of all three children being girls.

So, if we know that at least one of the children is a boy, the probability that all the children are boys is 1/8 divided by the probability of at least one boy. The probability of at least one boy is the complement of the probability of all three children being girls, which is 1 - 1/8 = 7/8.

Therefore, the probability of all three children being boys given that at least one of them is a boy is (1/8) / (7/8) = 1/7.