Re: Question about probability and number of cominations

On 26 mai, 11:40, "Matt " <x...@xxxxxxxxxxxx> wrote:
Euh<Euh...@xxxxxxxxxxx> wrote in message <972118fb-5cf2-4307-9c41-dcdb9b494...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>...
Let's say I have a boat with six places.

I have the probability distribution that there will be:

6 persons: p1 = 94 %
5 persons: p2 = 6 %
4 persons: p3 = 0 %
0 - 3 persons: = 0 %

They can sit randomly on the boat.

Now if the boat is cut in the middle to yield 2 boats of 3 places,
By doing a long enumeration, I found that the new probability
distribution is:

0 person: 0 %
1 person: 0 %
2 persons: 97.7 %
3 persons: 2.3 %

How can I get that result in a systematic way ?

Use Bayes' Rule. Let A be the number of people in a half-boat and B the number of people in the original,  complete boat. Then B

P(A=2)=P(A=2|B=6)*P(B=6)+ P(A=2|B=5)*P(B=5)+....

How would you evaluate this term: P(A=2|B=6) ?
.

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