Computing Probability

I've been working on stats for 13 hours. My brain is fried, my butt is asleep. I know this is simple. This is the last question I have to do. Can someone please show me how to do it and what the right answer should be???? Thank you.

If P(A) = 0.4, P(B | A) = 0.35, P(A È B) = 0.69, then P(B) =

What is P(A E B)?. A complement?.

Hello, suzychevy!

You must have used the wrong code.
I'll take a guess at what you meant.

\(\displaystyle P(A) = 0.4\quad P(B|A) = 0.35 \quad P(A \cup B) = 0.69\)

\(\displaystyle \text{Find: }\(B)\)

Click to expand...

\(\displaystyle \text{Bayes' Theorem: }\;P(B|A) \;=\;\frac{P(A \cap B)}{P(A)}\)

\(\displaystyle \text{So we have: }\;0.35 \;=\;\frac{P(A \cap B)}{0.4} \quad\Rightarrow\quad P(A \cap B) \:=\:0.14\)


\(\displaystyle \text{Formula: }\;P(A \cup B) \;=\;P(A) + P(B) - P(A \cap B)\)

\(\displaystyle \text{So we have: }\;\;0.69 \quad=\;\;\;0.4 \;\;+ P(B) \;\;-\;\; 0.14\)


\(\displaystyle \text{Therefore: }\;P(B) \;=\;0.69 - 0.4 + 0.14 \;=\;\boxed{0.43}\)