Question

A box contain 10 green pins 3 are blue and 7 are green. Two pins are randomly taken out of the box without replacement work out the probability that both pins are the same color

Answer 1

`P(Z)=(8)/(15)`

Explanation:

From the question we are told that:

Sample size
`n=10`

Green pins
`x=7`

Blue pins
`y=3`

Generally the probability of getting two green is mathematically given by

`P(2X)=(7)/(10)*(6)/(9)`

`P(2X)=(7)/(15)`

Generally the probability of getting two blue is mathematically given by

`P(2Y)=(3)/(10)*(2)/(9)`

`P(2Y)=(1)/(15)`

Therefore the probability that both pins are the same color P(Z)

`P(Z)=P(2Y)+P(2X)\\P(Z)=(7)/(15)+(1)/(15)`

`P(Z)=(8)/(15)`