Question

I only don't understand part d.

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 94% 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)? (Round your answer to four decimal places.)
p(2) =.8836 correct

(b) What is p(3)? [Hint: There are two different outcomes that result in Y = 3.]. (Round your answer to three decimal places.)
p(3) =.106 correct

(c) To have Y = 5, what must be true of the fifth battery selected?

The fifth battery must be an A.The fifth battery must be a U. correct

List the four outcomes for which Y = 5. (Enter your answer in set notation.)

{AUUUA, UUUAA, UAUUA, UUAUA}

correct

Determine p(5). (Round your answer to five decimal places.)
p(5) =.00076 correct

(d) Use the pattern in your answers for parts (a)–(c) to obtain a general formula for p(y).
p(y) =?

Answer 1

d)

p(y) =P(exactly one Acceptable in first (y-1) and 2nd acceptable on yth attempt)

=(_y-1C₁)*0.94²*0.06^y-2

=(y-1)*0.94²*0.06^y-2