Question

The probability of giving birth to a boy is 1/2. What is the probability that a family with 5 children will have at least 2 boys?

a)about 81.3%
b)about 76.9%
c)about 62.5%
d)about 90.3%

Answer 1

0.78

Explanation:

"The probability that a family with 5 children will have at least 2 boys" is equivalent to the complement 1 - P(family will have 1 or 0 boys).

We can use a calculator with statistical functions built in to calculate this probability. The function needed is for binomial probability: binom(n, p, x).

P(family will have 1 or 0 boys) = binomcdf(5, 0.5, {0, 1} ) produces two results: one the probab. of having 0 boys and one the probab. of having 1 boy: 0.03125 and 0.1875. We add these together, obtaining 0.21875.

Then we subtract this result from 1 to obtain The probability that a family with 5 children will have at least 2 boys: 1 - 0.21875 = 0.78125, which may be reasonably rounded off to 0.78.

Answer 2

81.3%.

Explanation:

This is Binomial probability.

Prob( Getting 1 boy) = 5C1 (1/2)^5

= 0.156

Prob ( Getting all girls = 5C5 (1/2)^5

= .031.

So Prob( at least 2 boys = 1 - (0.156 + 0.031)

= 0.813

= 81.3%.