Question

An urn contains 6 pink and 7 green balls. Five balls are randomly drawn from the urn in succession, with replacement. That is, aftereach draw, the selected ball is returned to the urn. What is the probability that all 5 balls drawn from the urn are green? Round your answer to three decimal places.

Answer 1

From the given question

There are a total of 13 balls (6 pink+7 green) and 5 balls will be selected from the urn.

Now,

$P(5\text{ gre}en\text{ balls)=}\frac{7}{13}\times\frac{7}{13}\times\frac{7}{13}\times\frac{7}{13}\times\frac{7}{13}$

Then,

$\begin{gathered} P(5\text{ gre}en\text{ balls)=}\frac{7}{13}\times\frac{7}{13}\times\frac{7}{13}\times\frac{7}{13}\times\frac{7}{13} \\ P(5\text{ gre}en\text{ balls)=(}\frac{7}{13})^5 \\ P(5\text{ gre}en\text{ balls)=}\frac{16807}{371293} \\ P(5\text{ gre}en\text{ balls)=}0.0453 \end{gathered}$

Hence, the probability that all 5 balls drawn from the urn are green is about 0.0453.