Chapter 6, Problem 8REAE

Solution

To find: the probability of getting 7 heads in 8 tosses of a coin.

The probability of getting 7 heads in 8 tosses of a coin is 0.03125.

Given:

A coin is tossed 8 times.

Concept used:

For a binomial experiment, the probability of $k$ successes in $n$ trails is,

  $P\left(k\text{successes}\right)=C{}_k{p}^k{\left(1-p\right)}^{n-k}$ , where $p$ is the probability of success.

  $C{}_r=\frac{n!}{r!\left(n-r\right)!}$

Calculation:

The probability of getting a head in tossing a coin is $p=0.5$.

Because the coin is tossed 8 times, $n=8$.

Now the probability of getting 7 heads is,

  $\begin{array}{c}P\left(k=7\right)=C{}_7{\left(0.5\right)}^7{\left(1-0.5\right)}^{8-7}\\ =\frac{8!}{7!\left(8-7\right)!}\times {\left(0.5\right)}^7{\left(0.5\right)}^1\\ =\frac{8\times \cancel{7!}}{\cancel{7!}\times 1}\times {\left(0.5\right)}^8\\ =\text{0}\text{.03125}\end{array}$