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%

0.78

Step-by-step 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.

81.3%.

Step-by-step 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%.