A new battery\'s voltage may be acceptable (A) or unacceptable (). A certain fla

Question

A new battery's voltage may be acceptable (A) or unacceptable (). A certain flashlight requires two batteries, so batteries will be independently selected and tested until two acceptable ones have been found. Suppose that 95% 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.) 0(2)-D9025 (b) What is p(3)? [Hint: There are two different outcomes that result in -3.]. (Round your answer to three decimal places.) (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. List the four outcomes for which Y-5. (Enter your answer in set notation.) Determine p(5). (Round your answer to five decimal places.) D(5) = (d) Use the pattern in your answers for parts (a(c) to obtain a general formula tor p(y) D(Y) -

Explanation / Answer

a)P(2 are tested)=P(first 2 both are acceptable)=0.95*0.95=0.9025

b)

p(3)=P(A then U then A)+P(U then A and then A)=0.95*(1-0.95)*0.95+(1-0.95)*0.95*0.95 =0.090

c)

the fifth battery nust be A

outcomes are { UUUAA, UUAUA , UAUUA , AUUUA}

p(5)=0.00045

d)

general formula P(y) =(y-1)*(0.05)y-2*(0.95)2

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