Probability

[匿名]

2010-12-18 5:45 am

Given that John takes bus today, probability that he takes bus tomorrow is 0.3. And given that John takes MTR today, probability that he takes MTR tomorrow is 0.5.
(a) If John takes bus on Dec 15, what is the probability that he takes MTR on Dec 16 and takes bus on Dec 17?
(b) If he takes bus on Dec 15, what is the probability that he takes bus on Dec 17?
(c) Suppose he takes bus on both Dec 15 and Dec 17, what is the probability that he takes MTR on Dec 16?
[Ans. (a) 0.35 (b) 0.44 (c) 0.7955]
Please explain in detail, not just giving the calculation, thanks.

回答 (1)

用戶9112

2010-12-18 6:24 am

✔ 最佳答案

(a) Probability that he takes MTR on Dec 16 is 1 – 0.3 = 0.7If he takes MTR on Dec 16, then probability that he takes bus on Dec 17 = 1 – 0.5 = 0.5The required probability = 0.7*0.5 = 0.35(b) Probability that he takes bus on Dec 16 is 0.3If he takes bus on Dec 16, then probability that he takes bus on Dec 17 = 0.3Probability of taking bus both days = 0.3*0.3 = 0.09Therefore required probability = 0.35 + 0.09 = 0.44(c) The conditional probability = 0.35 / 0.44= 0.7955

2010-12-17 22:29:21 補充：
(a) is bus : MTR : bus
(b) is bus : MTR : bus PLUS bus : bus : bus
(c) is bus : MTR : bus / (bus : MTR : bus + bus : bus : bus)

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