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?

• A. 0.004
• B. 0.006
• C. 0.216
• D. 0.994
• E. 0.996

Hint:

When calculating probabilities of independent events, first find the probability of the complementary event (failure) and subtract from 1.

Answer 1

Answer: (E)

To find the probability that Ramesh’s friend will receive the gift on time, we need to calculate the probability of the event where all four retailers deliver on time. The probability that each retailer fails to deliver on time: - Retailer A: $1 - 0.6 = 0.4$ - Retailer B: $1 - 0.8 = 0.2$ - Retailer C: $1 - 0.9 = 0.1$ - Retailer D: $1 - 0.5 = 0.5$ Now, the probability that all four retailers fail to deliver on time is the product of these probabilities: \[ \text{Failure probability} = 0.4 \times 0.2 \times 0.1 \times 0.5 = 0.004 \] Therefore, the probability that at least one retailer delivers on time is the complement of this: \[ \text{Success probability} = 1 - 0.004 = 0.996 \] \[ \boxed{0.996} \]