Chapter 11, Problem 18SGR

To determine

To find: The given experiment is a binomial experiment or not and hence find the probability.

Answer to Problem 18SGR

Theexperiment can be reduced to a binomial experiment, and the probability is $15.3\%$ .

Explanation of Solution

The correct answer is given as:

As in a binomial experiment each trial has only two possible outcomes, success or failure.

Since in the given experiments there are two possibilities are arising as either an adult is wearing watch or not.

Therefore, the given experiment can be reduced to a binomial experiment.

The probability of $X$ successes in $n$ independent trials is given as:

  $P\left(X\right)=C{}_X{p}^X{q}^{n-X}$

Here,

  $\begin{array}{l}n=25\\ X=20\\ p=0.74\\ q=0.26\end{array}$

Further simplified for the probability as:

  $\begin{array}{c}P\left(20\right)=C{}_{20}{\left(0.74\right)}^{20}{\left(0.26\right)}^5\\ \approx \frac{25!}{20!5!}\left(0.002\right)\left(0.001\right)\\ =0.153\\ =15.3\%\end{array}$