Chapter 13.2, Problem 7PPS

To determine

To find: the probability that Alfonso got $14$ tickets and Collin got $23$ tickets.

Answer to Problem 7PPS

The probability is $\frac{1}{2450}$ .

Explanation of Solution

Given:

Alfonso and Colin bought one raffle ticket at the state fair.

  $50$ tickets are randomly sold.

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, buying tickets is a way of arranging the people, order in this situation is important.

There are $50$ tickets. The number of possible outcomes in the sample space is the number of permutations of $50$ seats taken $2$ at as:

  $P{}_2=\frac{50!}{\left(50-2\right)!}=\frac{50\times 49\times 48!}{48!}=2450.$

Among these, there is only one particular arrangement in which Alfonso gets ticket $14$ and Colin gets ticket $23$ .

Hence, the probability is $\frac{1}{2450}$ .