Question

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) =

(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) =

(c) To have Y = 5, what must be true of the fifth battery selected? The fifth battery must be a U. The fifth battery must be an A.

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

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

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

Answer 1

a)P(Y=2) =P(first 2 are acceptable )=0.94*0.94=0.8836

b)P(3) =P(first 2 are acceptable)+P(exactly one of first 2 are acceptable and 3rd is acceptable)

=0.94*0.94+(2C1)*0.94^2*0.06=0.990

c)

The fifth battery must be an A.

four outcomes =AUUUA,UAUUA,UUAUA,UUUAA

p(5) =4*0.94^2*0.06^3=0.00076

d)

p(y)=(y-1)*0.94²*0.06^y-2