Chapter 5.2, Problem 40E

(a)

To determine

To find:

The sample space for tossing a fair coin $3$ times

Answer to Problem 40E

All possible sequences of outcomes $=2^3$

Explanation of Solution

Given:

The sample of a fair coin is $\left\{H,T\right\}$

Concept used:

Sample space:-In probability theory the sample space of an experiment or random trial is the set of all possible outcomes or result of that experiment

Calculation:

A sample space is usually denoted using set notation and the possible ordered outcomes are listed as element in the set

The sample space of a sequence of three fair cions is all possible sequences of outcomes $=2^3$

That is

The sample of a fair coin is $\left\{H,T\right\}$

  $\left\{HHH,HHT,HTH,HTT,THH,THT,TTH,TTT\right\}$

(b)

To determine

To find:

The assignment of probability to outcome tossing a fair coin in this sample space

Explanation of Solution

Given:

The sample of a fair coin flip is $\left\{H,T\right\}$

Concept used:

Sample space:-in probability theory the sample space of an experiment or random trial is the set of all possible outcomes or result of that experiment

A sample space is usually denoted using set notation and the possible ordered outcomes are listed as element in the set

Calculation:

The sample space of a sequence of three fair coins is all possible sequences of outcomes $=2^3$

That is

The sample of a fair coin flip is $\left\{H,T\right\}$

  $\left\{HHH,HHT,HTH,HTT,THH,THT,TTH,TTT\right\}$

Since the given sample space has $8$ outcomes and a fair coin is tossed three times

Therefore , the probability of all the event mentioned in the given sample space is same

Hence ,

The probability $=\frac{1}{8}$