Question

An urn contains 7 black and 9 red balls. Five 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 5 balls drawn from the urn areblack? Round your answer to three decimal places.

Answer 1

0.016

1) Considering that we have:

7 black balls

9 red balls

----------------------

16 balls

And 5 balls were randomly drawn.

2) We can write out:

As there was a replacement whenever we take a ball we put it back in the urn. Then the probability of taking 5 black balls is

`\begin{gathered} P(5\text{ black balls)=(}(7)/(16))^5=\text{ }(7)/(16)*(7)/(16)*(7)/(16)*(7)/(16)*(7)/(16) \\ P(5\text{ black balls) = 0.016} \end{gathered}`

3) Then the answer is 0.016