Chapter 13.6, Problem 20PPS

To determine

The probability that Wakim is not chosen to receive the free haircuts.

Answer to Problem 20PPS

The probability that Wakim is not chosen to receive the free haircuts is $92.5\%$ as $\frac{37}{40}$ .

Explanation of Solution

Given:

Total tickets: $80$

Randomly selected: $1$

In the raffle there are a total of $80$ tickets and Wakim has bought $6$ of these numbered tickets. If any of these $80$ tickets that matches one of the $6$ tickets with Wakim has, he get a free haircut but if any of these members does not match with Wakim’s he is not chosen to get a free haircut.

The probability that Wakim is not chosen to get free haircut is given as,

Fraction Form:

The probability of choosing a white marble in the fraction form is given as

  $\begin{array}{l}P\left(\text{not chosen to get a free haircut}\right)=\frac{\text{Total no}\text{.}\text{of}\text{tickets}-\text{no}\text{.}\text{of}\text{tickets}\text{that match with Wakim}}{\text{Total no}\text{.}\text{of}\text{tickets}}\\ P\left(\text{not chosen to get a free haircut}\right)=\frac{80-6}{80}\\ P\left(\text{not chosen to get a free haircut}\right)=\frac{74}{80}\text{or }\frac{37}{40}\end{array}$ Percent Form:

To convert from a fraction to the percent form, multiply the given fraction by 100 and finally place $\%$ at the end of the number. That is,

  $\begin{array}{l}=\left(\frac{37}{40}\right)\times 100\%\\ =\left(\frac{3700}{40}\right)\%\\ =92.5\%\end{array}$

Conclusion:

Hence, The probability that Wakim is not chosen to receive the free haircuts is $92.5\%$ as $\frac{37}{40}$ .