Quant Probability

Ramesh plans to order a birthday gift for his friend from an online retailer. However, the birthday coincides with the festival season during which there is a huge demand for buying online goods and hence deliveries are often delayed. He estimates that the probability of receiving the gift, in time, from the retailers A, B, C and D would be 0.6, 0.8, 0.9 and 0.5 respectively.

Playing safe, he orders from all four retailers simultaneously. What would be the probability that his friend would receive the gift in time?

  1. 0.004
  2. 0.006
  3. 0.216
  4. 0.994
  5. 0.996

Solution

You have to find the probability of receiving gift from at least one retailer.

Probability = 1 - (Probability of not receiving any gift)

The probabilities of not receiving the gift from retail A, B, C and D are 0.4, 0.2, 0.1 and 0.5, respectively.

Then probability of receiving gift from at least one retailer = {1 - (0.4×0.2×0.1×0.5)} = 0.996

The correct option is E.