XAT 2015 Quant & DI: Probability

This aptitude practice question appeared as a part of the quantitative reasoning and data interpretation section of the XAT 2015. A total of 33 questions appeared in this section in XAT 2015. This one is a medium level difficulty question and tests the concept of probability of exhaustive and complimentary events.

Question

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

  Correct Answer      Choice E. The probability of receiving a gift is 0.996.

Explanatory Answer

Key Data

1. Probability that retailer A will deliver the gift P(A) = 0.6
2. Probability that retailer B will deliver the gift P(B) = 0.8
3. Probability that retailer C will deliver the gift P(C) = 0.9
4. Probability that retailer D will deliver the gift P(D) = 0.5

His friend will receive the gift if at least one of the retailers delivers the gift.
Conversely, his friend will not receive the gift only if all four retailers fail to deliver the gift.

So, probability of receiving the gift = 1 – {probability of none of the retailers delivering the gift}

Probability that none of the retailers deliver

The probability of not receiving the gift from retailer A, P(A’) = 1 - P(A) = 1 - 0.6 = 0.4.
The probability of not receiving the gift from retailer B, P(B’) = 1 – 0.8 = 0.2
The probability of not receiving the gift from retailer C, P(C’) = 1 – 0.9 = 0.1
The probability of not receiving the gift from retailer D, P(D’) = 1 – 0.5 = 0.5

The probability that none of the retailers deliver the gift
= P(A’) * P(B’) * P(C’) * P(D’)
= (0.4 × 0.2 × 0.1 × 0.5)
=0.004

Therefore, the probability of Ramesh’s friend receiving a gift
= {1 - 0.004} = 0.996

  The correct answer is Choice E.

Video Explanation