Question

Conditional Probability can be calculated by

• A. \(P(B/A)=\frac{P(A\cap B)}{P(B)}\)
• B. \(P(A/B)=\frac{P(A\cap B)}{P(A\cap B)}\)
• C. \(P(A/B)=\frac{P(A\cap B)}{P(B)}\)
• D. \(P(A/B)=\frac{P(A\cap B)}{P(A)}\)

Hint:

For conditional probability, always remember: \(P(A/B)=\frac{P(A\cap B)}{P(B)}\). The denominator is the event after the slash.

Answer 1

The Correct Option is C

Concept: Conditional probability means the probability of occurrence of one event when another event has already occurred.

Step 1: Understand the meaning of \(P(A/B)\).
The notation \(P(A/B)\) means probability of event \(A\), given that event \(B\) has already occurred. \[ P(A/B)=\text{Probability of }A\text{ when }B\text{ is already known} \]

Step 2: Use the formula of conditional probability.
The formula is: \[ P(A/B)=\frac{P(A\cap B)}{P(B)} \] where, \[ P(A\cap B)=\text{Probability that both }A\text{ and }B\text{ occur} \] and \[ P(B)=\text{Probability of event }B \]

Step 3: Compare with the given options.
The correct formula exactly matches option (C). \[ P(A/B)=\frac{P(A\cap B)}{P(B)} \] Therefore, the correct answer is option (C).