A shipment of 10 television sets includes three that are def

A shipment of 10 television sets includes three that are defective. In how away ways can a hotel purchase four of these sets and receive at least two of the defective sets?

Solution

Here n= nor of television set =10

defectives =3

Prob for a defective = p = 0.3 and q =0.7

There are only two outcomes and also the defects are independent for each.

Hence X no of defectives follow a Binomial distribution with p =0.3, and n =no of trials = 4

P(X>=2) = Binomial cumulative prob for 2 =

0.3483

Hence prob for atleast 2 defective for 4 is 0.3483

No of ways this can be purchased is 10C4 ways(0.3483)

= 210(0.3483)

= 73.143 WAYS

Or in 73 ways this can be done.