Chapter 6.2, Problem 15E

Solution

To find: the probability of getting 12 heads in 20 tosses of a coin.

The probability of getting 12 heads in 20 tosses of a coin is 0.1201.

Given:

A coin is tossed 20 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 20 times, $n=20$ .

Now the probability of getting 12 heads is,

  $\begin{array}{c}P\left(k=12\right)=C{}_{12}{\left(0.5\right)}^{12}{\left(1-0.5\right)}^{20-12}\\ =\frac{20!}{12!\left(20-12\right)!}\times {\left(0.5\right)}^{12}{\left(0.5\right)}^8\\ =\frac{20\times 19\times 18\times 17\times 16\times 15\times 14\times 13\times \cancel{12!}}{\cancel{12!}\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}\times {\left(0.5\right)}^{20}\\ =\text{0}\text{.1201}\end{array}$