Question

To the right are the outcomes that are possible when a couple has three children. Refer to that? list, and find the probability of each event.a. Among three? children, there are exactly 3 girlsb. Among three? children, there are exactly 2 boysc. Among three? children, there are exactly 0 boysa. What is the probability of exactly 3 girls out of three? children?b. What is the probability of exactly 2 boys out of three children?c. what is the probability of exactly 0 boys out of three children.LIST TO REFER TO:1st 2nd 3rdboy boy boyboy boy girlboy girl boyboy girl girlgirl boy boygirl boy girlgirl girl boygirl girl girl

Answer 1

a)
`(1)/(8)`

b)
`(3)/(8)`

c)
`(1)/(8)`

Explanation:

Sample space for the given case is:

S: {BBB, BBG, BGB, GBB, BGG, GBG, GGB, GGG}

n(S) = 8

where B is boy and G is girl and the position stands for first, second and third respectively.

Formula:

`\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}`

a) probability of exactly 3 girls

C = {GGG}

`P(\text{Exactly 3 girls)} = (n(C))/(n(S)) = (1)/(8)`

b) probability of exactly 2 boys out of three children

C: { BBG, BGB, GBB}

`P(\text{Exactly 2 boys)} = (n(C))/(n(S)) = (3)/(8)`

c) probability of exactly 0 boys out of three children

C = {GGG}

`P(\text{Exactly 0 boys)} = (n(C))/(n(S)) = (1)/(8)`