Chapter 7, Problem 1RE

In Exercises 1–6, say how many elements are in the sample space S, list the elements of the given event E, and compute the probability of E.

Three coins are tossed; the result is one or more tails.

To determine

To calculate: The probability that the result is one or more tails when three coins are tossed, after finding the number of elements in the sample space S.

Answer to Problem 1RE

Solution:

There are 8 elements in the sample space S and the probability that the result is one or more tails when three coins are tossed is $\frac{7}{8}$.

Explanation of Solution

Given Information:

A coin is tossed three times and the sample space for the tossing of coin is S.

Formula used:

According to the formula for probability, the probability of event E, which has $n\left(E\right)$ possible outcomes out of $n\left(S\right)$ total outcomes is

$P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}$

Calculation:

Consider the event of tossing getting one or more tails to be E.

When a coin is tossed, there are two possible outcomes, heads and tails. Thus, the total possible outcomes when three coins are tossed are

$\begin{array}{c}n\left(S\right)=2\cdot 2\cdot 2\\ =2^3\\ =8\end{array}$

The set with one or more tails is,

$E=\left\{\text{HHT,HTH,THH,TTH,THT,HTT,TTT}\right\}$

Thus, the number of possible outcomes for one or more tails is

$n\left(E\right)=7$

Apply the formula for probability and substitute 7 for $n\left(E\right)$ and 8 for $n\left(S\right)$,

$P\left(E\right)=\frac{7}{8}$

Hence, the probability that the result is one or more tails when three coins are tossed is $\frac{7}{8}$.