Chapter 9, Problem 100RE

To determine

To find: Probability of getting at least one tail.

Answer to Problem 100RE

The probability of obtaining at least one tail when a coin is tossed 5 times is $\frac{1}{32}$ .

Explanation of Solution

Given:

Suppose a coin is tossed 5 times

Suppose a coin is tossed 5 times

Since the number of outcomes in a single toss of a coin is 2

Therefore, when a coin is tossed 5 times, then the total numbers of possible outcomes are

  $\begin{array}{l}n\left(S\right)=2^5\hfill \\ =32\hfill \end{array}$

Assume that $E$ denotes the event that at least one tail appears.

Then the complement of the event $E$ , denoted by $E\text{'}$ represents the event that no tail appears

Also there will be no tail when all the tosses results in head and it happens only once.

Therefore, the number of favorable cases to $E\text{'}$ is 1

That is

  $n\left(E_1^{\text{'}}\right)=1$

Hence, the number of elements favorable to the event $E$ is

  $\begin{array}{l}\begin{array}{l}n\left(E\right)=32–n\left(E\right)\hfill \\ =32–1\hfill \end{array} \\ =31\end{array}$

So probability of obtaining at least one tail

  $\begin{array}{l}P\left(E\right)=\left[\frac{n\left(E\right)}{n\left(S\right)}\right] \\ =\frac{31}{32}\end{array}$

Hence, the probability of obtaining at least one tail when a coin is tossed 5 times is $\frac{1}{32}$ .