Maths Statistics

2015-04-27 5:40 am

In a canteen, the probabilities that apple will be contained in a main dish and a juice are 20% and 16%, respectively. In addition, the probability that apple will be contained in the main dish or the juice is 30%.

On Saturdays, the probability that apple will be contained both in the main dish and juice is 21%. It is assumed that the restaurant is opened 7 days per week. In a randomly selected day, it is found that apple is contained in both the main dish and the juice. What is the probability that the day is a Saturday?

Can anyone help me? I don't know how to do

回答 (1)

polarbearhmh

2015-04-27 6:14 am

✔ 最佳答案

On saturdays,
P (apple in main dish AND juice) = 0.21

Not on saturdays,
P(apple in main dish) = 0.2, P(apple in juice) = 0.16, P(apple in main dish OR juice) = 0.3
∴ P(apple in main dish AND juice) = P(A in M) + P(A in J) - P(A in M/J)
= 0.2 + 0.16 - 0.3 = 0.06

In a randomly selected day,
P(It's Saturaday and A in M&J) = P(Sat) × P(A in M&J) = 1/7 × 0.21 = 0.03
P(A in M&J) = P(It's Saturaday and A in M&J) + P(It's not Saturaday and A in M&J)
= 0.03 + 6/7 × (0.06) = 0.57/7

∴ P(given A in M&J, it's Sat) = P(It's Saturaday and A in M&J)/P(A in M&J)
= 0.03 / (0.57/7)
= 7/19

參考: The answer is 7/19

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