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

Pls help with this question pls using the factorial “!”-example-1
User Wtlucy
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1 Answer

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27 votes

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}
User YoYo
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