# What is the probability of having atleast one boy in a family of 3 children?

2
by kareen

2015-03-02T17:09:10+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
If the family has 3 children, then they can be
{BBB, BBG, BGB, GBB, BGG, GBG, GBB, GGG}

total number of combinations = 8
number of combinations with atleast one boy = 7

Probability(atleast one boy) = 7/8
why 7 came?
2015-03-02T17:18:22+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Some times it is simpler to calculate the contrary of the event and its probability and then subtract it from 1 to get our answer.
=====================
The probability of one child being a boy = 1/2      a girl = 1/2
Let us assume that the 3 children being boys or girls are independent events.

Event of having no boys at all
= first child is a girl   AND    2nd child is a girl   AND  3rd girl is a girl.

P(no boys among 3 children) = 1/2 * 1/2 * 1/2 = 1/8
P(there is at least one boy among 3 children)  = 1  - 1/8 = 7/8