Question 1174251
p(b given a) = p(a and b) / p(a)


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.