Question

Suppose that in a family of a taxi association chairperson in Lephalale, Matlou's family, the probability that the will have a girl is 0.3 . Suppose that in their family there are 6 children, What will be the probability that a) Their children are all boys b) Atleast 2 of their children are girls c) They have exacly three girls d) all their children are girls.

Answer 1

To find the probabilities, we can use the binomial probability formula and the given information about the probability of having a girl in Matlou's family.

Step-by-step explanation:

To find the probability that all of the children in Matlou's family are boys, we need to calculate the probability of having a boy for each child and multiply those probabilities together. Since the probability of having a girl is 0.3, the probability of having a boy is 1 - 0.3 = 0.7. So, the probability of all boys would be 0.7 ^ 6 = 0.1176.

To find the probability that at least 2 of their children are girls, we need to calculate the probability of having 2, 3, 4, 5, or 6 girls and add those probabilities together. The probability of having exactly k girls out of 6 children can be calculated using the binomial probability formula: P(X = k) = (6 choose k) * (0.3^k) * (0.7^(6-k)). Summing these probabilities from k = 2 to k = 6 will give us the desired probability.

To find the probability that they have exactly three girls, we can calculate P(X = 3) using the binomial probability formula.

Finally, to find the probability that all of their children are girls, we calculate P(X = 6) using the binomial probability formula.