A company owns 400 labtops. Each laptop has an 8% probability of not working. Yo

Question

A company owns 400 labtops. Each laptop has an 8% probability of not working. You randomly select 20 laptops for your sales people.
A. What is the likelihood that 5 will be broken? B. What is the likelihood that they will all work? C. What is the likelihood that they will all be broken? D. What is the likelihood that at least 18 of them will work? A company owns 400 labtops. Each laptop has an 8% probability of not working. You randomly select 20 laptops for your sales people.
A. What is the likelihood that 5 will be broken? B. What is the likelihood that they will all work? C. What is the likelihood that they will all be broken? D. What is the likelihood that at least 18 of them will work?
A. What is the likelihood that 5 will be broken? B. What is the likelihood that they will all work? C. What is the likelihood that they will all be broken? D. What is the likelihood that at least 18 of them will work?

Explanation / Answer

The random variable X follows binomial with parameters n=200, p=0.08

20 laptops are selected.

A.P(X=5)

=20C5*0.08^5*(1-0.08)^(20-5)

=0.014

B.P(all will work)

=20C0*0.08^0*(1-0.08)^20

=0.188

C.P(all will be broken)

=0.08^20

=<0.000001

D.P(at least 18 will work)

=P(X>=18)

=20C18*(1-0.08)^18*(0.08)^2+...+20C20*(1-0.08)^20*(0.08)^0

=0.787

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