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, ?

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

c. To have , what must be true of the fifth battery selected? List the four outcomes for which and then determine p(5).

d. Use the pattern in your answers for parts (a)–

(c) to obtain a general formula for p(y).

Y 5 5 Y 5 5 Y 5 3 P(Y 5 2)

P(X # 0)

F(0) 5 p(y) 5 y y 5 1,

c, 5 2

/50 a

5 y51 p(y) 5 1 p(y) 5 ky y 5 1, . . . , 5 Y 5 the number