Chapter 6.8, Problem 6E

i.

To determine

To make a tree diagram to show all the different possible outcomes.

Answer to Problem 6E

  

Explanation of Solution

Given:

Three coins are flipped.

Calculation:

The tree diagram with the possible outcomes can be drawn as:

  

The different possible outcomes are HHH,HHT,HTH,HTT,THH,THT,TTH,TTT.

ii.

To determine

To find how many different possible outcomes are there.

Answer to Problem 6E

There are total of $8$ different possible outcomes.

Explanation of Solution

Given:

Three coins are flipped.

Calculation:

The tree diagram with the possible outcomes can be drawn as:

  

As conclude from the tree diagram there are total of $8$ different possible outcomes,

HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.

Hence,

There are total of $8$ different possible outcomes.

iii.

To determine

The find favorable outcomes.

Answer to Problem 6E

There are $2$ favorable outcomes.

Explanation of Solution

Given:

Three coins are flipped.

Calculation:

The tree diagram with the possible outcomes can be drawn as:

  

As from the tree diagram,

The favorable outcomes which shows all three coins heads or all three coins tails is HHH and TTT.

Hence,

There are $2$ favorable outcomes.

iv.

To determine

To find the probability.

Answer to Problem 6E

The probability of getting all three coins heads or all three coins tails is $\frac{1}{4}$ .

Explanation of Solution

Given:

Three coins are flipped.

Calculation:

The tree diagram with the possible outcomes can be drawn as:

  

The probability of getting all three coins heads or all three coins tails is:

  $=$ probability of getting all three heads $+$ probability of getting all three tails

  $\begin{array}{l}=\frac{1}{8}+\frac{1}{8}\\ =\frac{2}{8}=\frac{1}{4}\end{array}$

Hence,

The probability of getting all three coins heads or all three coins tails is $\frac{1}{4}$ .