Please do help me complete this question Not sure what do do

Please do help me complete this question.

Not sure what do do.

Thanks in advance

A new battery\'s voltage may be acceptable (A) or unacceptable (U). A certain flashlight requires two batteries, so batteries will be independently selected and tested until two acceptable ones have been found. Suppose that 95%of all batteries have acceptable voltages. Let y denote the number batteries that must be tested.

Solution

Let p be the probability of getting a good battery.

As given , p=0.95 .

Let Y be the no. of batteries to be tested to have two good batteries.

Y ~ Negative Binomial( p ) .

The P.M.F of Y is

f(y) = (y-1)*p²*(1-p)^y-2 , for all y=2,3,... ; =0 , otherwise . ....................(**)

## The Outcomes for which Y=5 is true is,

{ (U,U,U,A,A ) ; (U,U,A,U,A) ; (U,A,U,U,A) ; (A,U,U,U,A) } ,the last one must be an \'A\' - battrey to stop the trials of testing the betteries.

## P(5) = P(Y=5) = (5-1)p²*(1-p)^5-2 =0.00045125 = 0.00045 (approximately)

## The general formula of P(y) is given above in f(y) [ the P.M.F of Y (**) ]