Chapter 13.2, Problem 10PPS

To determine

To find: the probability that the Jimmy was selected first and George second.

Answer to Problem 10PPS

The probability is $\frac{1}{90}$ or $1\%$ .

Explanation of Solution

Given:

Two people are chosen randomly from a group of ten..

Concept used:

The probability formula is used to compute the probability of an event to occur as:

  $P\left(A\right)=\frac{\text{Number of favorable outcome}}{\text{Total Number of favorable outcomes}}$ .

According to the permutation formula:

  $P{}_r=\frac{n!}{\left(n-r\right)!}.$

Where $P$ is the permutations.

  $n$ is the total number of objects in the set.

  $r$ is the total number of objects in the set.

Calculation:

Since, choosing people is a way of ranking the members, order in this situation is important. The number of possible outcomes in the sample space is the number of permutations of $10$ people taken $2$ at a time is $P{}_2$ .

  $P{}_2=\frac{10!}{\left(10-2\right)!}=\frac{10!\times 9!\times 8!}{8!}=90.$

Among these,there is only one particular arrangement in which Jimmy is selected first and George second. Therefore, the probability is $\frac{1}{90}$ .

Hence, the probability is $\frac{1}{90}$ or $1\%$ .