Question

An urn contains 6 green and 5 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 green? Round your answer to three decimal places.

Answer 1

Probability of all 4 balls drawn should be green equal to ≈
`0.089`.

Explanation:

Given that,

An urn contains 6 green and 5 pink balls.

Now, Total number of balls in urn is
`6+5=11` balls.

Four balls are randomly drawn from the urn in succession, with replacement.

So, probability of green ball =
`(6)/(11)`

Again, there is a condition that,

Probability all 4 balls drawn should be green.

Then, P(all 4 balls should be green)=
`(6)/(11) * (6)/(11) * (6)/(11)* (6)/(11)`

=
`((6)/(11) )^(4) = (6^(4) )/(11^(4) )`

=
`(1296)/(14641) = 0.08851`

≈
`0.089`

Therefore,

Probability of all 4 balls drawn should be green equal to ≈
`0.089`.