A person has undertaken a minning job the probability of completion of job on time with or without rain are 0.42 and 0.90 respectively .if the probability that it will rain is 0.45 the mining job will be completed on time
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1. If it rains,
probability to rain = 0.45
probability to complete the work in time(rains) = 0.42
probability to complete the work when it rains
= (0.45) × (0.42)
= 0.189
2. If not rains,
probability to not rain = 1 - probability to rain
= 1 - 0.45
= 0.55
probability to complete the work in time (not rains) = 0.90
probability to complete the work when it not rains
= 0.55 × 0.90
= 0.495
Total probability to complete the work whether it rains or not = 0.189 + 0.495
= 0.684
So, probability to complete the work in time = 0.684
Hope, this helps you
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