Math Help - statistics 1 book miscellaneous exercise question

1. statistics 1 book miscellaneous exercise question

Two events are A and B are such that P(A)= 3/4 , P(B l A)= 1/5 , and P(B' l A')= 4/7 find a) P(A l B) b) P(B) c) P(A l B) any help would be great!

2. Originally Posted by arowland
Two events are A and B are such that P(A)= 3/4 , P(B l A)= 1/5 , and P(B' l A')= 4/7 find a) P(A l B) b) P(B) c) P(A l B) any help would be great!
I suggest drawing a tree diagram. Then you will see that

(a), (c) (They're the same question!) $\Pr(A \, | \, B) = \frac{ \left( \frac{3}{4} \right) \cdot \left( \frac{1}{5} \right) }{\left( \frac{3}{4} \right) \cdot \left( \frac{1}{5} \right) + \left( \frac{1}{4} \right) \cdot \left( \frac{3}{7} \right) } = \, ....$

(b) $\Pr(B) = \left( \frac{3}{4} \right) \cdot \left( \frac{1}{5} \right) + \left( \frac{1}{4} \right) \cdot \left( \frac{3}{7} \right) = \, ....$