Chapter 10.7, Problem 17HP

To determine

To find:Compare and contrast the theoretical probability with the experimental probability.

Answer to Problem 17HP

The experimental probability of picking a Navy blue socks is

  $30\%$ while the theoretical probability is about $20\%$ .So picking a navy pair of socks in the experimental occurred more often than its expected.

Explanation of Solution

Given information: White pair $8$ ,Black pair $5$ ,Navy pair $7$ ,Khaki pair $3$ ,Others pair $12$

Theoretical Probability:

  $P(\mathrm{navy}\mathrm{socks})=\frac{\mathrm{frequency}\mathrm{of}\mathrm{navy}\mathrm{socks}}{\mathrm{total}\mathrm{frequency}}$

  $\begin{array}{l}=\frac{7}{8+5+7+3+12}\\ =\frac{7}{35}or20\%\end{array}$

  $\mathrm{Experimental}\mathrm{Probability}=\frac{\mathrm{Number}\mathrm{of}Navy\mathrm{socks}\mathrm{out}\mathrm{of}\mathrm{total}\mathrm{number}\mathrm{of}\mathrm{selections}}{\mathrm{Total}\mathrm{selections}\mathrm{of}socks}$

  $=\frac{6}{20}or30\%$