Question 1174251: Events A and B are dependent. P(A)= 5/12
and P(B given A) = 6/11. Find P(A and B).
Appreciate the help :D Found 3 solutions by ikleyn, Theo, MathTherapy:Answer by ikleyn(52788) (Show Source):
You can put this solution on YOUR website! .
Events A and B are dependent. P(A)= 5/12
and P(B given A) = 6/11. Find P(A and B).
~~~~~~~~~~~~~
P(B given A) is the conditional probability.
The standard classical designation for it is P(B|A).
So, P(B given A) is the same as P(B|A).
By the definition, P(B|A) = P(B ∩ A) / P(A).
So, you are GIVEN that
P(B ∩ A) / P(A) = , or, which is the same,
P(B ∩ A) : = .
THEREFORE,
P(B ∩ A) = = = . ANSWER
you have p(a) = 5/12 and you have p(b given a) = 6/11.
formula becomes 6/11 = p(a and b) / (5/12)
multiply both sides of this equation by (5/12) to get:
(6/11) * (5/12) = p(a and b).
simplify to get 30/132 = p(a and b).
simplify further to get 5/22 = p(a and b)
your solution is p(a and b) = 5/22.
confirm by replacing p(a and b) in the original equation to get:
p(b given a) = p(a and b) / p(a) becomes 6/11 = 5/22 / (5/12).
this becomes 6/11 = 5/22 * 12/5 which becomes 6/11 = 12/22.
simplify to get 6/11 = 6/11 which is true.
this confirms the value of p(a and b) is good.
