An analysis of the causes of employee lateness in arrival at a large office show

Question

An analysis of the causes of employee lateness in arrival at a large office shows that the probability that an employee will be late because of an automobile breakdown is 0.03. The probability that the office manager correctly attributes a late arrival to an automobile breakdown is 0.80, and the probability that the office manager incorrectly attributes a late arrival to an automobile breakdown is 0.05. What is the probability that a late arrival attributed to an automobile breakdown by the office manager is actually due to an automobile breakdown?

Explanation / Answer

P(Automative breakdown) = 0.03

So,

P(No Breakdown) = 1 - 0.03 = 0.97

P(Late arrival attributed to automative breakdown | Automative breakdown) = 0.8

P(Late arrival attributed to automative breakdown | No automative breakdown) = 0.05

We need to find:

P(Automative breakdown | Late arrival attributed to automative breakdown).

From Baye's theorem,

P(Automative breakdown | Late arrival attributed to automative breakdown)

= (0.03* 0.8)/ (0.97* 0.05 + 0.03* 0.8)

= 0.331

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