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The probability that event $A$ occurs is $P(A) = 0.4$. $B$ is an event independent of $A$ and $P(A \hbox{ or } B \hbox{ or both})$ = $0.7$. Find $P(B)$.

I gave this a go but saw that there were two unknowns which are $P(B)$ and $P(A\cap B)$. I couldn't work out how to get either. Any help on this problem will be much appreciated.

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    Hint: Use the fact that A and B are independent – 2017-01-22

2 Answers 2

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You have in general that:

$P(A \cup B) = P(A) + P(B) - P(A \cap B)$

And since $A$ and $B$ are independent, you have $P(A \cap B) = P(A)*P(B)$

So given that you know $P(A \cup B)$ and $P(A)$ you can solve for $P(B)$.

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If the events are independent, $P(A \wedge B) = P(A)P(B)$. So you really still only have 1 unknown: $P(B)$, the quantity that you can then solve for.