7.109 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 80% of all batteries have acceptable voltages, and let y denote the number of batteries that must be tested.

a. What is p(2), that is, P(y 5 2)?

b. What is p(3)? (Hint: There are two different outcomes that result in y 5 3.)

c. In order to have y 5 5, what must be true of the fifth battery selected? List the four outcomes for which y 5 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).