Chapter 12.7, Problem 11PPS

a.

To determine

To find the probability that any three coins will show tails.

Answer to Problem 11PPS

The probability of three coins showing tails is $\frac{1}{5}$ .

Explanation of Solution

Given information:

The given statement is:

“Toss $4$ coins, one at a time, $20$ times, and record the number of heads and tails. Find each probability based on the results.”

From the observation, it is seen that three coins showed tails for $4$ times.

The probability of three coins showing tails is be shown by:

  $\text{P}\left(\text{any three coins will show tails}\right)=\frac{4}{20}=\frac{1}{5}$

Hence, the probability of three coins showing tails is $\frac{1}{5}$ .

b.

To determine

To find the probability that any two coins will show heads.

Answer to Problem 11PPS

The probability of two coins showing heads is $\frac{3}{10}$ .

Explanation of Solution

Given information:

The given statement is:

“Toss $4$ coins, one at a time, $20$ times, and record the number of heads and tails. Find each probability based on the results.”

From the observation, it is seen that two coins showed heads for $6$ times.

The probability of two coins showing heads is be shown by:

  $\text{P}\left(\text{any two coins will show heads}\right)=\frac{6}{20}=\frac{3}{10}$

Hence, the probability of two coins showing heads is $\frac{3}{10}$ .

c.

To determine

To find the probability that first coin will show heads and the last coin will show tails.

Answer to Problem 11PPS

The probability of two coins showing heads is $\frac{3}{10}$ .

Explanation of Solution

Given information:

The given statement is:

“Toss $4$ coins, one at a time, $20$ times, and record the number of heads and tails. Find each probability based on the results.”

From the observation, it is seen that first coins showed heads and last coin showed tails for $2$ times.

The probability of two coins showing heads is be shown by:

  $\text{P}\left(\text{first coin show heads and fourth coin show tails}\right)=\frac{2}{20}=\frac{1}{10}$

Hence, the probabilitythat first coin will show heads and the last coin will show tails is $\frac{1}{10}$ .