Chapter 13.4, Problem 22HP

(a)

To determine

To design the simulation that could be used to predict the probability that exactly $3$ of the coins will be tails.

Explanation of Solution

Given:

In an experiment, five coins flipped simultaneously.

Calculation:

The following is the simulation of five coins flipped simultaneously.

[,1] [,2] [,3] [,4] [,5]

[1,] "h" "h" "h" "h" "h"

[2,] "h" "h" "h" "h" "t"

[3,] "h" "h" "h" "t" "h"

[4,] "h" "h" "h" "t" "t"

[5,] "h" "h" "t" "h" "h"

[6,] "h" "h" "t" "h" "t"

[7,] "h" "h" "t" "t" "h"

[8,] "h" "h" "t" "t" "t"

[9,] "h" "t" "h" "h" "h"

[10,] "h" "t" "h" "h" "t"

[11,] "h" "t" "h" "t" "h"

[12,] "h" "t" "h" "t" "t"

[13,] "h" "t" "t" "h" "h"

[14,] "h" "t" "t" "h" "t"

[15,] "h" "t" "t" "t" "h"

[16,] "h" "t" "t" "t" "t"

[17,] "t" "h" "h" "h" "h"

[18,] "t" "h" "h" "h" "t"

[19,] "t" "h" "h" "t" "h"

[20,] "t" "h" "h" "t" "t"

[21,] "t" "h" "t" "h" "h"

[22,] "t" "h" "t" "h" "t"

[23,] "t" "h" "t" "t" "h"

[24,] "t" "h" "t" "t" "t"

[25,] "t" "t" "h" "h" "h"

[26,] "t" "t" "h" "h" "t"

[27,] "t" "t" "h" "t" "h"

[28,] "t" "t" "h" "t" "t"

[29,] "t" "t" "t" "h" "h"

[30,] "t" "t" "t" "h" "t"

[31,] "t" "t" "t" "t" "h"

[32,] "t" "t" "t" "t" "t"

(b)

To determine

To find out whether the simulation can be used to predict the probability that at least three coins will be of tails.

Answer to Problem 22HP

Yes.

Explanation of Solution

Given:

In an experiment, five coins flipped simultaneously.

Calculation:

Ye, the simulation can be used to predict the probability that at least three coins will be of tails.

(c)

To determine

To find out the probability that exactly three of the coins will be tails.

Answer to Problem 22HP

  $0.31$ .

Explanation of Solution

Given:

In an experiment, five coins flipped simultaneously.

Calculation:

The required probability is −

  $\begin{array}{l}C(5,3){\left(\frac{1}{2}\right)}^3{\left(\frac{1}{2}\right)}^2\\ =10\times {\left(\frac{1}{2}\right)}^5=0.31\end{array}$