Question

A forest contains$20$elk, which $5$are captured, tagged, and then released. A certain time later,$4$the $20$elk are captured. What is the probability that $2$these $4$have been tagged? What assumptions are you making?

Short answer

The probability that $2$these $4$have been tagged is$\frac{70}{323}$.

Step-by-step solution

Given Information.

A forest contains $20$elk, which $5$are captured, tagged, and then released. A certain time later, $4$the $20$elk are captured.

Explanation.

We choose $2$from the $5$tagged in $\left(\begin{array}{l}5\\ 2\end{array}\right)$ways and $2$from the remaining $15$untagged ones in $\left(\begin{array}{c}15\\ 2\end{array}\right)$ways. This way we get the total possible arrangements of the desired property. We divide this by the total arrangements of $4$elks possible i.elocalid="1648915063779" $\left(\begin{array}{c}20\\ 4\end{array}\right)$.

Explanation.

The probability that$2$these$4$have been tagged is$\frac{70}{323}$.