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 91% 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).