Writex Brown, an E-commerce company gives home delivery of its valuable products, after receiving final order in their website, by different modes of transportation like bike, scooter, tempo and truck. The probabilities of using bike, scooter, tempo and truck are respectively 2/9, 1/9, 4/9, and 2/9. The probabilities of delivering the product late to the destination by using these modes of transport are 3/5, 2/5, 1/5, and 4/5. If the product reaches the destination in time, find the probability that the company has used scooter to reach the destination.
Explanation:
This is a case of conditional probability.
The product being delivered on time implies no delay in delivering the product.
P(Scooter | No Delay) = [P(Scooter and No Delay Using Scooter] / [P(No Delay)]
[P(Scooter and No Delay] = P(Scooter) × P(No Delay Using Scooter)
= (1/9) × [1 − (2/5)] = (1/9) × (3/5) = 3/45
P(No delay) = [(2/9) × (2/5)] + [(1/9) × (3/5)] + [(4/9) × (4/5)] + [(2/9) × (1/5)]
= (4/45) + (3/45) + (16/45) + (2/45) = 25/45
∴ Required probability = (3/45) / (25/45) = 3/25
Hence, option (c).
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