Question

what does the notation p(b|a) mean?
choose the correct answer below.
a. the probability of event a occurring, given that event b has occurred
b. the probability of event b occurring, divided by the probability of event a occurring
c. the probability of event b occurring, given that event a has occurred
d. the probability of both event a and event b occurring

Explanation:

In probability, the notation \(P(B|A)\) represents conditional probability. The vertical bar "|" is read as "given". So, \(P(B|A)\) means the probability of event \(B\) occurring under the condition that event \(A\) has already occurred.

• Option A is incorrect because it has the events reversed (\(P(A|B)\) would be the probability of \(A\) given \(B\)).
• Option B is incorrect as \(P(B|A)=\frac{P(A\cap B)}{P(A)}\) (when \(P(A)>0\)), not simply \(P(B)\div P(A)\).
• Option D is incorrect because \(P(A\cap B)\) is the probability of both \(A\) and \(B\) occurring, without the "given" condition.

Answer:

C. The probability of event B occurring, given that event A has occurred