Question

Pls help with this question pls using the factorial “!”

Answer 1

Given:

Probability of employees that are smokers = 35% = 0.35

Number of workers chosen random = 6

Required: Probability that there will be exactly 2 smokers

Let X denotes the number of smokers. Then X follows B(6, 0.35).

It is enough to find P(X = 2).

The binomial distribution is defined as

`P(X=x)=^nC_xp^xq^(n-x)`

Substitute the given values.

`P(X=x)=^6C_x(0.35)^x(0.65)^(6-x)`

To find P(X =2), plug 2 for x .

`\begin{gathered} P(X=2)=^6C_2(0.35)^2(0.65)^4 \\ =(6!)/(2!4!)\cdot(0.0219) \end{gathered}`