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 90% of all batteries have acceptable voltages. Let Y denote the number of batteries that must be tested.
a. What is p (2), that is, P(Y = 2)?
b. What is p (3)? [Hint: There are two different outcomes that result in Y = 3.]
c. To have Y = 5, what must be true of the fifth battery selected? List the four outcomes for which Y = 5 and then determine p(5).
d. Use the pattern in your answers for parts (a)-(c) to obtain a general formula for p(y).