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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?
The probability that his friend receives the gift in time will be when his friend receives even one gift.
That can be calculated as the probability of his friend receiving at least one gift.
The probability that none of the retailers sends in time = $$(1 - 0.6) \times (1 - 0.8) \times (1 - 0.9) \times (1 - 0.5)$$
= $$0.4 \times 0.2 \times 0.1 \times 0.5 = 0.004$$
$$\therefore$$ Probability of his receiving at least one gift = $$1 - 0.004 = 0.996$$
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