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Question
Sun October 21, 2012 By: Thomas Albin

# Martin throws two dice spontaneously.If the sum of the outcomes is 12,he offers lunch at a five star hotel with probability 2/3. If the sum is 7,he offers lunch with probability 1/2.In all other cases,he offers lunch with probability 1/3.Given that the lunch was offered,the probability that the sum of the outcomes equals 12 is a)1/18 b)1/20 c)1/24 d)1/36

Tue November 20, 2012

this question is based on bayes theorem

We have to calculate that the lunch was offered, what is the probability that the sum of the outcomes equals 12.As lunch can be offered in three cases that sum was 12,that sum was 7 or else sum of number on the two dices.

Applying bayes theorem,

P(12/L)=probability that 12 was the sum when lunch was offered.

P(7/L)=probability that 7 was the sum when lunch was offered.

P(O/L)=probability that sum  was other than 7,12  when lunch was offered.

Here, we have:

chance that sum will be 12=1/36,only(6,6) pair

chance that sum will be7=6/36,   (6,1),(5,2), (4,3) ,(3,4),(2,5),((1,6)

Remaining cases=36-7=29 chance for these cases=29/36

P(12/L)= 2/3*1/36+ ½*6/36+1/3*29/36

=1/20
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