Chapter 5.1, Problem 32E

To determine

To find:

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

Answer to Problem 32E

All possible sequences of outcomes $=2^3$

Explanation of Solution

Given:

The sample space 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 five fair cions flips is all possible sequences of outcomes $=2^5$

That is

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

  $\left\{HHHHH,HHHHT,HHHTH,HHTHH,HTHHH,THHHH\mathrm{........}TTTTT\right\}$

The probability that the result of the next flip will be tails is always $=0.5$

It does not matter if past results were $\left\{TTTTT\right\}or\left\{HHHHH\right\}or\left\{THTHT\right\}$

The probability that the next will be tails is still $0.5$ in each of these cases and in every other cases

Hence the option (a) is correct