Chapter 8.6, Problem 13E

To determine

To find the probability of getting at least one head.

Answer to Problem 13E

The probability of getting at least one head is $\frac{7}{8}$ .

Explanation of Solution

Given:

A coin is tossed three times.

Calculation:

The sample of the experiment of tossing a coin three times is, $S=\left\{\text{HHH}\text{,}\text{HHT}\text{,}\text{THH}\text{,}\text{HTH}\text{,}\text{HTT}\text{,}\text{THT}\text{,}\text{TTH}\text{,}\text{TTT}\right\}$

Where H and T represents head and tail respectively.

Now let Gis the event of getting at least one head is,

  $G=\left\{\text{HHH}\text{,}\text{HHT}\text{,}\text{THH}\text{,}\text{HTH}\text{,}\text{HTT}\text{,}\text{THT}\text{,}\text{TTH}\right\}$

Hence the probability of getting at least one head is,

  $\begin{array}{l}P\left(G\right)=\frac{n\left(G\right)}{n\left(S\right)}\\ \Rightarrow P\left(G\right)=\frac{7}{8}\end{array}$