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 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.) p(2) = 0.9025 (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) = 0.090 (c) To have Y = 5, what must be true of the fifth battery selected? The fifth battery must be an A. O The fifth battery must be a U. List the four outcomes for which Y = 5. (Enter your answer in set notation.) |{UUUAA, UAUUA,UUAUA,AUUUA} Determine p(5). (Round your answer to five decimal places.) p(5) = 0.00045 (d) Use the pattern in your answers for parts (a)-(c) to obtain a general formula for p(y). P(V) = (.9)²(.1)"-2. (y– 1)
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 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.) p(2) = 0.9025 (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) = 0.090 (c) To have Y = 5, what must be true of the fifth battery selected? The fifth battery must be an A. O The fifth battery must be a U. List the four outcomes for which Y = 5. (Enter your answer in set notation.) |{UUUAA, UAUUA,UUAUA,AUUUA} Determine p(5). (Round your answer to five decimal places.) p(5) = 0.00045 (d) Use the pattern in your answers for parts (a)-(c) to obtain a general formula for p(y). P(V) = (.9)²(.1)"-2. (y– 1)
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Chapter1: Combinatorial Analysis
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I need help with 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 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.)
p(2) = 0.9025
(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) = 0.090
(c) To have Y = 5, what must be true of the fifth battery selected?
The fifth battery must be an A.
O The fifth battery must be a U.
List the four outcomes for which Y = 5. (Enter your answer in set notation.)
{UUUAA, UAUUA,UUAUA AUUUA}
Determine p(5). (Round your answer to five decimal places.)
p(5) = 0.00045
(d) Use
pattern in your answers for parts (a)-(c) to obtain a general formula for p(y).
p(v) = (.9)²(.1)"2. (y – 1)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff8536f70-6afb-49b2-94d8-7d5f9820999c%2Fa888dab4-ca84-4221-8561-144e477e222a%2F2f2tsw_processed.png&w=3840&q=75)
Transcribed Image Text: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 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.)
p(2) = 0.9025
(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) = 0.090
(c) To have Y = 5, what must be true of the fifth battery selected?
The fifth battery must be an A.
O The fifth battery must be a U.
List the four outcomes for which Y = 5. (Enter your answer in set notation.)
{UUUAA, UAUUA,UUAUA AUUUA}
Determine p(5). (Round your answer to five decimal places.)
p(5) = 0.00045
(d) Use
pattern in your answers for parts (a)-(c) to obtain a general formula for p(y).
p(v) = (.9)²(.1)"2. (y – 1)
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