# Answer to Question #7599 in Abstract Algebra for diganta

Question #7599

The probability that a bulb produced by a factory will fuse after certain period of time is 0.05. Find the probability that out of 5 such bulbs

a. None fuses

b. Not more than 2 fuse

c. More than 2 fuse

a. None fuses

b. Not more than 2 fuse

c. More than 2 fuse

Expert's answer

The probability that a bulb produced by a factory will fuse after certain period of time is 0.05. Find the probability that out of 5 such bulbs

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a. None fuses

P(None fuses) = (1-0.05)^5 = 0.95^5 = 0.7738

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b. Not more than 2 fuse

P(Not more than 2 fuse) = P(0 fuses) + P(1 fuses) + P(2 fuses) = ...

P(0 fuses) = 0.95^5

P(1 fuses) = 0.05*(1-0.05)^4

P(2 fuses) = 0.05^2*(1-0.05)^3

... = 0.95^5 + 0.05*(1-0.05)^4 + 0.05^2*(1-0.05)^3 = 0.8167.

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c. More than 2 fuse

P(More than 2 fuse) = 1 - P(Not more than 2 fuse) = 1-0.8167 = 0.1833.

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a. None fuses

P(None fuses) = (1-0.05)^5 = 0.95^5 = 0.7738

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b. Not more than 2 fuse

P(Not more than 2 fuse) = P(0 fuses) + P(1 fuses) + P(2 fuses) = ...

P(0 fuses) = 0.95^5

P(1 fuses) = 0.05*(1-0.05)^4

P(2 fuses) = 0.05^2*(1-0.05)^3

... = 0.95^5 + 0.05*(1-0.05)^4 + 0.05^2*(1-0.05)^3 = 0.8167.

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c. More than 2 fuse

P(More than 2 fuse) = 1 - P(Not more than 2 fuse) = 1-0.8167 = 0.1833.

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