Question

Probability that worker work is 0.2 out of 4 .What is the probability that atleast 3 will work? and What is the probability that exactly 3 work?

Answer 1

I we take X as the number of workers work,

P(X=1) = 0.2

Then for P(X>=3) = P(X=3) + P(X=4)

We can easily write for P(X=3) as 0.2 x 0.2 x 0.2 x 0.8 because there are 4 workers, three have to work and other do not work.

P(X=3) = 0.2 x 0.2 x 0.2 x 0.8

           = 0.0064

Wait! Forgot something?

Since there are 4 workes and we are choosing 3 to work and one to not to work. We have to use combinations in order to find the number of ways we can pick these 3 workers.

So 4C3 = 4!/(4-3)! . 3!

            = 4

Then the total probability of only three workers will work = 4C3 x P(X=3)

                                                                                               = 4 x 0.0064

                                                                                               = 0.0256

For P(X=4) =  0.2 x 0.2 x 0.2 x 0.2 , All for has to work

                 = 0.0016

Then the probability of at least 4 workers wok

P(X>=3) = 4C3 xP(X=3) + P(X=4)

             = 0.0256 + 0.0016

             = 0.0272

On the above we already find the probability of exactly 3 workers work,

Which is 4C3 x P(X=3) = 0.0256