Chapter 12.3, Problem 19PPS

(a)

To determine

To Find: The probability that a game is an action game, given that it is not a sports or role playing game.

Answer to Problem 19PPS

The required probability is 0.3731.

Explanation of Solution

Given:

  

The probability that game sold by a company is not a sports or role playing game is,

  $\begin{array}{cc}P(\text{not a sports or role playing})& =1-(0.17+0.16)\\ & =0.67\end{array}$

And the probability that game sold by a company is an action game not a sports or role playing game is,

  $P\left(anactionandnotasportsorroleplaying\right)=0.25$

The probability that game sold by a company is an action game given that it is not a sports or role playing game is,

  $\begin{array}{l}P\left(\begin{array}{l}\text{an action}\mid \text{not a}\hfill \\ \text{sports or role playing}\hfill \end{array}\right)=\frac{P\left(\begin{array}{l}\text{an action and not a}\hfill \\ \text{sports or role playing}\hfill \end{array}\right)}{P(\text{not a sports or role playing})}\\ \begin{array}{l}=\frac{0.25}{0.67}\hfill \\ =0.3731\hfill \end{array}\end{array}$

Hence, the required probability is 0.3731.

(b)

To determine

To Find:Tthe probability that a game is a family game, given that it is not a strategy or action game.

Answer to Problem 19PPS

The required probability is 0.1429.

Explanation of Solution

The probability that game sold by a company is not a strategy or action game is,

  $\begin{array}{l}P\left(notastrategygameoractiongame\right)=1–\left(0.19+0.25\right)\hfill \\ =0.56\hfill \end{array}$

And the probability that game sold by a company is a family game and not a strategy game or action game is,

  $P\left(\begin{array}{l}\text{a family game and not a}\hfill \\ \text{strategy game or action game}\hfill \end{array}\right)=0.08$

The probability that game sold by a company is a family given that it is not a strategy or action game is,

  $\begin{array}{l}P\left(\begin{array}{l}\text{a family game}\mid \text{not a}\hfill \\ \text{strategy or action}\hfill \end{array}\right)=\frac{P\left(\begin{array}{l}\text{a family game and not a}\hfill \\ \text{strategy or action game}\hfill \end{array}\right)}{P(\text{not a strategy or action game})}\\ \begin{array}{l}=\frac{0.08}{0.56}\hfill \\ =0.1429\hfill \end{array}\end{array}$

Hence, the required probability is 0.1429.