Tom goes to school by taxi on 1/4 of the school days and by MTR on the rest. The probability of being late for school by traveling of taxi and MTR are1/20 and1/30 respectively. Given that Tom is late for school on one day, find the probability that he travels by MTR on that day.
THANKS FOR HELP1
maths-probability
2009-04-03 8:12 am
回答 (2)
2009-04-03 8:46 am
✔ 最佳答案
Denote:
T = Tom goes to school by taxi
M = Tom goes to school by MTR
L = Tom is late
P(T) = 1/4
P(M) = 1 - (1/4) = 3/4
P(L|T) = P(L and T)/P(T)
1/20 = P(L and T)/(1/4)
P(L and T) = 1/80
P(L|M) = P(L and M)/P(M)
1/30 = P(L and M)/(3/4)
L(L and M) = 1/40
P(L)
= P(L and T) + P(L and M)
= (1/80) + (1/40)
= 3/80
P(M|L)
= P(M and L)/P(L)
= (1/40)/(3/80)
= 2/3
=
2009-04-03 8:47 am
The conditional probability = (3/4*1/30) / (1/4*1/20 + 3/4*1/30) = 2/3
收錄日期: 2021-04-29 18:17:24
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