A couple decided to have 4 children. What is the probability that they will have at least two boys?

Solution:

Given: A couple has 4 children

Let P be the probability of having at least, 2 boys

The probability of having a boy is 1/2 and that of a girl is 1/2

Each of the 4 children can either be a boy or a girl.

Therefore, total number of outcomes(O) = 2⁴ =16

No. of outcomes such that at least 2 out of 4 children are boys can be given by:

(p) = ⁴C₂+ ⁴C₃+ ⁴C₄

= 6 + 4 + 1

= 11

Probability P = No. of favorable outcomes(p)/Total no. of outcomes(O) = 11/16

Therefore, the probability that they will have at least two boys is 11/16

A couple decided to have 4 children. What is the probability that they will have at least two boys?

Summary:

If a couple decided to have 4 children then the probability that they will have at least two boys is 11/16.