Chapter 14.1, Problem 18E

To determine

To find: Theprobability that only 6 will survive.

Answer to Problem 18E

The required probability is $0.293$ .

Explanation of Solution

Consider that the rate of survival of the variety of mums is 80% that is the probability of 0.8.

The objective is to determine the probability that only 6 will survive out of 8 mums planted..

Consider that the survival of the mum is success of each of the planted mum then the probability is,

  $p=0.8$

Then, the probability of the failure in each of the trial is,

  $\begin{array}{c}q=1-p\\ =1-0.8\\ =0.2\end{array}$

Then, the probability that there are only six success is obtained by the binomial theorem as,

  $\begin{array}{c}P\left(6\right)=C\left(8,6\right){\left(0.8\right)}^6{\left(0.2\right)}^{8-6}\\ =\frac{8!}{\left(8-6\right)6!}{\left(0.8\right)}^6{\left(0.2\right)}^2\\ =\frac{8\cdot 7\cdot 6!}{2!6!}\left(0.2621\right)\cdot \left(0.04\right)\\ =0.293\end{array}$