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Delivery Probability of Online Retailers

XAT 2015 · Quantitative Ability & Data Interpretation · Easy · Probability

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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. A.

    0.004

  2. B.

    0.006

  3. C.

    0.216

  4. D.

    0.994

  5. E.

    0.996

Answer

E

Explanation

The probability that his friend receives the gift in time is 1−P(none of the four deliver in time)1 - P(\text{none of the four deliver in time}).

P(none deliver in time)=(1−0.6)×(1−0.8)×(1−0.9)×(1−0.5)P(\text{none deliver in time}) = (1 - 0.6) \times (1 - 0.8) \times (1 - 0.9) \times (1 - 0.5) =0.4×0.2×0.1×0.5=0.004= 0.4 \times 0.2 \times 0.1 \times 0.5 = 0.004.

Probability of receiving at least one gift in time =1−0.004=0.996= 1 - 0.004 = 0.996.

Hence, option E is correct.

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