Q. 2.33 - A First Course in Probability

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?

Step-by-Step Solution

Answer

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

Step 1 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.

Step 2 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.e$\left(\begin{array}{c}20\\ 4\end{array}\right)$.

Step 3 Explanation.

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