Chapter 13.4, Problem 16PPS

(a)

To determine

To calculate the expected value for each roll.

Answer to Problem 16PPS

The average value is $47$ and the expected value is $45.3$ .

Explanation of Solution

Given:

The probability that Susana will get $100$ points in a roll is $20\%$ , $200$ points in a roll is $55\%$ , $300$ points in a roll is $20\%$ and $400$ points in a roll is $5\%$

Calculation:

The following is the required table-

Outcome	Frequency
Red	5
Blue	16
White	29
Total	50

The average value is $47$

And the expected value is $45.3$

(b)

To determine

To design a simulation and estimate Susana’s average value for this game.

Answer to Problem 16PPS

The average value is $47$ and the expected value is $45.3$ .

Explanation of Solution

Given:

The probability that Susana will get $100$ points in a roll is $20\%$ , $200$ points in a roll is $55\%$ , $300$ points in a roll is $20\%$ and $400$ points in a roll is $5\%$

Calculation:

The following is the required table-

Outcome	Frequency
Red	5
Blue	16
White	29
Total	50

The average value is $47$

And the expected value is $45.3$

(c)

To determine

To compare the values in parts a and parts b.

Answer to Problem 16PPS

The average value is $47$ and the expected value is $45.3$ .

Explanation of Solution

Given:

The probability that Susana will get $100$ points in a roll is $20\%$ , $200$ points in a roll is $55\%$ , $300$ points in a roll is $20\%$ and $400$ points in a roll is $5\%$

Calculation:

The following is the required table-

Outcome	Frequency
Red	5
Blue	16
White	29
Total	50

The average value is $47$

And the expected value is $45.3$