Question

An urn contains 7 green and 8 pink balls. Four balls are randomly drawn from the urn in succession, with replacement. That is, after each draw, the selected ball is returned to the urn. What is the probability that all 4 balls drawn from the urn are pink? Round your answer to three decimal places.

Answer 1

`0.081`

Explanation:

GIVEN: An urn contains
`7` green and
`8` pink balls. Four balls are randomly drawn from the urn in succession, with replacement. That is, after each draw, the selected ball is returned to the urn.

TO FIND: What is the probability that all 4 balls drawn from the urn are pink.

SOLUTION:

Total balls in urn
`=15`

Total green balls
`=7`

Total pink balls
`=8`

probability of getting a pink ball
`=\frac{\text{total pink balls}}{\text{total balls}}`

`=(8)/(15)`

As selected ball is returned to the urn, therefore drawing a ball is an independent event.

probability of getting all
`4` balls pink
`=(8)/(15)*(8)/(15)*(8)/(15)*(8)/(15)`

`=(4096)/(50625)`

`=0.081`

Hence the probability that all 4 balls drawn from the urn are pink is
`0.081`