Binomial Distribution (MathM1)
2011-07-16 2:54 am
Two 16-seater minibuses, A and B, are awaiting at a station. A and B have already had 11 and 12 seats occupied respectively. Each passenger selects A with probability 4/7 and selects B with probability 3/7. Find the probability that A is filled up first. Please show your solution with detailed explanation. Thanks! ;)
回答 (2)
2011-07-16 3:42 am
✔ 最佳答案
A : 16 - 11 = 5 seatsB : 16 - 12 = 4 seatsP(E) = P(The first 5 passengers select 5A)
+ P(The first 5 passengers select 4A1B and the 6th selects A)
+ P(The first 6 passengers select 4A2B and the 7th selects A)
+ P(The first 7 passengers select 4A3B and the 8th selects A)= (4/7)⁵
+ 5C4 * (4/7)⁴(3/7) * (4/7)
+ 6C4 * (4/7)⁴(3/7)² * (4/7)
+ 7C4 * (4/7)⁴(3/7)³ * (4/7)= 434176 / 823543= 0.5272
2011-07-15 22:29:46 補充：
Thanks for your comment.
2011-07-16 5:00 am
P(The first 5 passengers select 4A1B and the 6th selects A)=5C4 * (4/7)⁴(3/7) * (4/7)
the meaning of words is not so clear,
it is better to use P(4 passengers among the first 5 passengers select A and the remaing one selects B and the 6th passenger selects A)
the meaning of words is not so clear,
it is better to use P(4 passengers among the first 5 passengers select A and the remaing one selects B and the 6th passenger selects A)
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