Chapter 7.1, Problem 7.18E

(a)

To determine

To Explain: the assumptions for the chance behaviour involved in this setting.

Answer to Problem 7.18E

Independent draws, constant probability of success

Explanation of Solution

Given:

Rock-paper-scissors

Assuming that there are two players arbitrary select one of the three options rock, paper and scissors and also needs that each card has the same chance of being choosing

It also requires that the two individuals make their decisions independent.

(b)

To determine

To Explain: that assign digits to represent outcomes.

Answer to Problem 7.18E

Rock: Digit 1

Paper: Digit 2

Scissors: Digit 3

Ignore: Digits 0, 4, 5, 6, 7, 8, 9

Explanation of Solution

Given:

There are 3 options: rock, paper and scissors

Assigning 1 number to rock, 1 number to paper and 1 number to scissors

Rock: Digit 1

Paper: Digit 2

Scissors: Digit 3

Ignore: Digits 0, 4, 5, 6, 7, 8, 9

(c)

To determine

To Calculate: the estimate probability and simulate 20 repetitions using your calculator or Table B.

Answer to Problem 7.18E

0.7

Explanation of Solution

Formula used:

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

Calculation:

Using the calculator generating one game using TI 83/TI 84 calculator

  $randInt\left(1,3,2\right)$

If the two digits are different then the game resulted in a winner and Repeating this 20 more time.

No winner, Winner, Winner, Winner, Winner, Winner, Winner, Winner, No winner, No winner, No winner, Winner, Winner, Winner, Winner, Winner, Winner, Winner, No winner, No winner

There are 14 out of 20 games resulted in a winner.

  $\begin{array}{c}\text{Probability}\text{=}\frac{\text{Favourable Cases}}{\text{Total}\text{Cases}}\\ \text{P}\left(\text{Winner}\right)\text{=}\frac{\text{14}}{\text{20}}\\ \text{=0}\text{.7}\end{array}$

Therefore the estimate probability is 0.7 (may vary)