Probability Example

In a lot of pen drives three are defective. A customer picks four pen drives simultaneously from the lot

at random . Find the probability of the pen drives selected will not be defective where the lot size is 30?

The required probability = (the number of ways choosing four pen drives which are not defective )/(total number of ways of choosing four pen drives)

we can use combination in such case;

Out of 30 there are three defectives pen drives that means 27 are non defective or o.k.

Now combination of selecting four object at a time out of 27.

i.e. 27 C 4

By solving this we get 27!/(4!( 27-4)! ) = (27 x 26 x 25 x 24 x 23!)/(4 x 3 x 2 x 1 x 23! )

= (27 x 26 x 25 x 24 x 23!)/(4 x 3 x 2 x 1 x 23! )

= 17550

Total Number of ways of selecting four objects out of 30 ;

i.e. 30C 4 ; solving this we get 30! /(4!( 30-4)! ) = (30 x 29 x 28 x 27 x 26!)/(4 x 3x2x1 x 26! ) = (30 x 29 x 28 x 27 x 26!)/(4 x 3x2x1 x 26! )

= 27405