Conditional Probability Negation

Question

I have the probabilities of event A, event B, and event ( A ∩ B ). The conditional probability equation allows me to find the probability of event A given event B, and the probability of event B given event A. However, how would I find the probability of event A given event B does not happen?

Answer 1

Hint: Use the following relations.

• $P(A\cap \overline B)=P(A)-P(A\cap B)$
• $P(\overline B)=1-P(B)$
• $P(A|\overline B)=\frac{P(A\cap \overline B)}{P(\overline B)}$

The table below make it easier to find such relations.

\begin{array}{c|c|c} & A&\overline A \\ \hline B & A\cap B &\overline A\cap B& \\ \hline \overline B&A\cap \overline B&\overline A\cap \overline B& \\ \hline & && 1 \\ \end{array}