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Interperting a solution involving conditional probability.

  • #1

Homework Statement

a family consisting of a father, mother, and a child is chosen at random and is asked on what day of the week each of them was born. What is the probability that all three were born on different days given that the father was born on a monday?

Solution: A is the even all three were born on different days. B is the event that the father was born on a monday. n(A and B)=6P2=30 and n(B)=7*7=49. So P(A|B)=30/49



Homework Equations


P(A|B)=P(A and B)/P(B).
P(A|B) reads: probability of A given B.



The Attempt at a Solution


Really, what i dont get is why for n(B), we get 7*7. I mean it should be 52 since there are 52 weeks in a year=>52 mondays in a year. I just don't get the solution that was given.
 

Answers and Replies

  • #2
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n(B) is the number of possibilities for the days for the father, mother, and child, without requiring that all three be born on different days, given that dad was born on Monday. So, 1 choice for dad, 7 choices for mom, 7 choices for kid. 1*7*7=49.

n(A and B) is 1*6P2
 

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