Sunday Sons
A man says “One of my two sons was born on Sunday.” What is the probability that both of his sons are born on Sunday?
If this probability can be expressed as , where and are coprime positive integers, submit your answer as .
The answer is 14.
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1 solution
Labeling the days of the week 1,2,3,4,5,6,7 (sunday = 1), we look at all the possibilities with at least 1 sunday: 11 12 13 14 15 16 17 21 31 41 51 61 71
You can see that there is a 1/13 chance of the configuration 1,1.
Alternatively, using Baye’s theorem
A = Both children are born on sunday
B = A son is born on sunday
P(B|A) = 1
P(A) = 1/49
P(B) = 1/7+1/7 - 1/49 = 13/49
=P(A|B) = 1/13