Question

what does the notation p(b|a) mean?

choose the correct answer below.

a. the probability of both event a and event b occurring
b. the probability of event b occurring, divided by the probability of event a occurring
c. the probability of event a occurring, given that event b has occurred
d. the probability of event b occurring, given that event a has occurred

Explanation:

Define the notation

Using the Dependent Events knowledge point

$$ P(B|A) $$

represents the conditional probability of event \(B\) occurring given that event \(A\) has already occurred.

Evaluate the options

• Option A describes the joint probability, \(P(A \text{ and } B)\).
• Option B describes the formula ratio \(\frac{P(B)}{P(A)}\), which is not the definition of the notation itself.
• Option C describes \(P(A|B)\), where event \(B\) is the given condition.
• Option D correctly describes \(P(B|A)\), where event \(A\) is the given condition.

Answer:

• A. The probability of both event A and event B occurring
• B. The probability of event B occurring, divided by the probability of event A occurring
• C. The probability of event A occurring, given that event B has occurred
• D. The probability of event B occurring, given that event A has occurred (Correct answer)