Chapter 13.6, Problem 25HP

To determine

The experimental and theoretical probability of the jasmine’s socks.

Answer to Problem 25HP

The experimental probability of picking a Navy socks is $\text{30\%}$ while the theoretical probability is about $\text{20\%}$ .

Explanation of Solution

Given:

White Pairs: $8$

Black Pairs: $5$

Navy Pairs: $7$

Khaki Pairs: $3$

Other Pairs: $12$

The theoretical probability:

  $\begin{array}{l}P\left(\text{Navy}\text{Socks}\right)=\frac{\text{Frequency}\text{of}\text{Navy}\text{socks}}{\text{Total}\text{Frequency}}\\ P\left(\text{Navy}\text{Socks}\right)=\frac{7}{8+5+7+3+12}\\ P\left(\text{Navy}\text{Socks}\right)=\frac{7}{35}\text{or}20\%\end{array}$

Experimental Probability:

  $\begin{array}{l}P\left(\text{Navy}\text{Socks}\right)=\frac{\text{No}\text{. of }\text{Navy}\text{socks out of total no}\text{. of selections}}{\text{Total}\text{selection}\text{of}\text{socks}}\\ P\left(\text{Navy}\text{Socks}\right)=\frac{6}{20}\text{or 30\%}\end{array}$

Conclusion:

Hence, so the experimental probability of picking a Navy socks is $\text{30\%}$ while the theoretical probability is about $\text{20\%}$ . So, picking a navy pair of socks in the experiment occurred more often than it expected.