Question

(a) A lamp has two bulbs of a type with an average lifetime of 1800 hours. Assuming that we can model the probability of failure of these bulbs by an exponential density function with mean μ = 1800, find the probability that both of the lamp's bulbs fail within 2000 hours.

(b) Another lamp has just one bulb of the same type as in part (a). If one bulb burns out and is replaced by a bulb of the same type, find the probability that the two bulbs fail within a total of 1000 hours.

Answer 1

a) 0.45

b) 0.11

Step-by-step explanation:

A) P( both bulbs fail within 2000 hours ) = 0.45

Given data:

Average lifetime of bulbs = 1800 hours

mean μ = 1800

b) P( both bulbs fail within 1000 hours ) =

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