Chapter 6.1, Problem 34E

To determine

To Calculate: the mean amount that researcher wins

Answer to Problem 34E

0.15

Explanation of Solution

Given:

Total number of cards = 52

Card of aces = 4

If win get $10 and at loss $1

Formula used:

  $\text{Probability}\text{=}\frac{\text{Favourable Cases}}{TotalCases}$

  $\mu ={\displaystyle \sum x\text{P}\left(x\right)}$

Calculation:

Probability of getting Ace cards which means probability of winning

  $\text{P}\left(win\right)=\frac{4}{52}=\frac{1}{13}$

Probability of not getting Ace cards which means probability of losing

  $\text{P}\left(loss\right)=\frac{48}{52}=\frac{12}{13}$

  $\begin{array}{c}\mu ={\displaystyle \sum x\text{P}\left(x\right)}\\ =\$10\times \frac{1}{13}+\left(-\$1\right)\times \frac{12}{13}\\ =\$\frac{2}{13}\\ =0.15\end{array}$

Hence, the correct option is (c)