Calculating Conditional Probability: A and B Events with A' and B' Notation

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To calculate the probability of event B given that event A does not occur, the formula P(B|A') = P(B n A')/P(A') is appropriate. Given that P(A) is 0.7, P(A') equals 0.3. The probability P(B n A') can be derived from the provided probabilities, considering the relationship between events A and B. Utilizing Bayes' theorem can further clarify the calculations. Understanding these concepts is crucial for accurately determining conditional probabilities in related events.
Homewoodm01
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An event A has a 70% chance of occurring, an event B has a 40% of occurring and the event (A n B) has a 20% chance of occurring. The events are not unrelated.

If A does not occur what is the probability of B?

notation A' means (not A)

I have tried to use the formula P(B|A') = P(B n A')/P(A')


However Not sure if that's the right way to go and if A' would be equal to .3.

Please Help :)
 
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Thanks for the link, I have used one of Baye's laws hopefully that helps give me the right answer.
 
I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...
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