Chapter 13.6, Problem 26STP

To determine

The probability that a randomly selected toy manufactured at the company will not have a defect.

1. $\text{7\%}$
2. $\text{70\%}$
3. $\text{27\%}$
4. $\text{93\%}$

Answer to Problem 26STP

The correct option is, D. $\text{93\%}$

Explanation of Solution

In a manufacturing company, the production records show that $\text{5}$ out of every $\text{75}$ toys are defective. That also means the rest of the toys $75-5=70$ are not defective.

So with the help of all of the ratio the probability that the randomly selected toy will not have a defect is given as,

The fraction form:

The probability that the randomly selected toy will not have a defect is given is

  $\begin{array}{l}P\left(\text{Not to have defect}\right)=\frac{\text{Total}\text{no}\text{.}\text{of}\text{defects}}{\text{Total}\text{no}\text{.}\text{of}\text{Toys}}\\ P\left(\text{Not to have defect}\right)=\frac{75-5}{75}\\ P\left(\text{Not to have defect}\right)=\frac{70}{75}\text{or}\frac{14}{15}\end{array}$

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,

  $\begin{array}{l}=\left(\frac{14}{15}\right)\times 100\%\\ =\left(\frac{1400}{15}\right)\%\\ =93.33\%\text{or}93\%\end{array}$

Conclusion:

Hence the correct option is, D. $\text{93\%}$