Refer to Exercise 17 for the definition of a k out of n

Step1 of 4:

Let us consider a random variable X it presents the number of components function properly on a rainy season.Then X follows binomial distribution with parameters “n and p” that is 

\(\mathrm{X} \sim \mathrm{B}(\mathrm{n}, \mathrm{p}), The probability mass function of binomial distribution is given by

\(P(X)=\left(\begin{array}{l} n \\ x \end{array}\right) p^{x}(1-p)^{n-x}, \mathrm{x}=0,1,2, \ldots, \mathrm{n}\)

Where,

\(\begin{aligned} \mathrm{n} & =\text { sample size } \\ & =6 \\ \mathrm{x} & =\text { random variable } \\ \mathrm{p} & =\text { probability of success } \\ & =\text { Probability that the each component is function on rainy season } \\ & =0.70 \\ \mathrm{q} & =1-\mathrm{p} \text { (probability of failure) } \\ & =1-0.70 \\ & =0.30 \end{aligned}\)

Here our goal is:

a.We need to find the probability that the system functions on a rainy day.

b.We need to find the probability that the system functions on a non-rainy da