A well-equipped turtle habitat should have several different components. Suppose

Question

A well-equipped turtle habitat should have several different components. Suppose one suclh habitat has a heat bulb which has probability .2 of burning out within a year, an overhead lamp that burns out within a year with probability .6, a power filter for water that breaks within a year with probability .1, and an automatic feeder that breaks within a year with probability .8. Further suppose that these breakages are independent of each other. (a) What is the probability that none of these components will break within a year? (b) What is the probability that exactly three components will break within a year?

Explanation / Answer

Following are the given prob.

P(Heat bulb burn out) = 0.2

P(Overhead lamp burn out ) = 0.6

P(Power filter breakage ) = 0.1

P(automatic feeder breakage) = 0.8

a. P( none of the components will break) = [1-P(Heat bulb burn out)]*[ 1-P(Overhead lamp burn out )]*[1-P(Power filter breakage )]*[1-P(automatic feeder breakage)]

= 0.8*0.4*0.9*0.2 = 0.0576

b. P(exactly 3 components will break) = P(Heat bulb,Overhead lamp and Power filter will break) + P(Heat bulb,Overhead lamp and automatic feeder will break) +P(Heat bulb ,Power filter and automatic feeder will break) +P(Overhead lamp,Power filter and automatic feeder will break)

= 0.2*0.6*0.1 + 0.2*0.6*0.8 + 0.2*0.1*0.8 + 0.1*0.6*0.8

=0.172

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