Question

g To the right are the outcomes that are possible when a couple has three children. Assume that boys and girls are equally​ likely, so that the eight simple events are equally likely. Find the probability that when a couple has three​ children, there is exactly 1 boy. 1st 2nd 3rd boy minus boy minus boy boy minus boy minus girl boy minus girl minus boy boy minus girl minus girl girl minus boy minus boy girl minus boy minus girl girl minus girl minus boy girl minus girl minus girl What is the probability of exactly 1 boy out of three​ children?

Answer 1

the probability of getting a boy is out of three children is
`=(3)/(8)`

Explanation:

Given That,

1st 2nd 3rd

Boy Boy Boy

Boy Boy Girl

Boy Girl Boy

Boy Girl Girl

Girl Boy Boy

Girl Boy Girl

Girl Girl Boy

Girl Girl Girl

Probability occur of an event (A) is define as

`P(A)=\frac{\text {Favourable event occured}}{\text {Total of the event}}`

A is the event of getting 1 boy out of three children

here there are total possible outcomes = 8

number of favourable outcomes of 1 boy =3

hence,

probability = favourable outcome/total outcome

`=(3)/(8)`

Therefore, the probability of getting a boy is out of three children is
`=(3)/(8)`

Answer 2

3 in 8 or 37.5%

Explanation:

It is know that the sample space for the event of having three children has 8 possible outcomes. In order to have EXACTLY one boy, either the first children is a boy and the other two are girls, the second one is a boy and the other two are girls, or the first two are girls and the last children is a boy.

Therefore, there is a 3 in 8 probability that the couple will have exactly one boy:

`P=(3)/(8)=0.375=37.5\%`

The probability is 3 in 8 or 37.5%.