Assuming that the probability that a boy will be born is 12

Assuming that the probability that a boy will be born is 1/2 and that the chance for a girl is also 1/2, answer the following questions

a. If four babies are born in a given hospital on the same day, what is the probability that all four will be boys?

b. What is the probability that three will be boys and one a girl?

c. What is the probability that two will be boys and two girls?

d. What combination of boys and girls among the four babies is most likely to occur? Why?

e. What is the probability that if a fifth child is born it will be a boy? A girl?

Solution

a). (1/2)⁴ = 1/16

b). ⁴C₃ * (1/2)³ * (1/2) = 4 * 1/16 = 1/4

c). ⁴C₂* (1/2)² * (1/2)² = 12 * 1/16 = 3/4

d). Two boys and two girls. Because total number of possibilities are 2⁴ which is 16 and ⁴C₂which is 12 are the no. of possibilites for 2 boys and 2 girls. This case hence has the maximum probability.

e). Since the birth of each child is independent, the probability of 5th child to be a BOY = 1/2 and the probability of 5th child to be a GIRL = 1/2