Question

Let \( E \) be an event of a sample space \( S \) of an experiment, then \( P(S | E) \) is:

• A. \( P(S \cap E) \)
• B. \( P(E) \)
• C. \( 1 \)
• D. \( 0 \)

Hint:

The probability of the sample space given any event is always 1, as the sample space includes all outcomes.

Answer 1

The Correct Option is C

Step 1: Understanding conditional probability.
The conditional probability \( P(A | B) \) is defined as: \[ P(A | B) = \frac{P(A \cap B)}{P(B)}, \quad \text{provided } P(B)>0. \] Step 2: Apply to \( P(S | E) \).
Here, \( A = S \) (the sample space), and \( B = E \). Since \( S \) contains all possible outcomes: \[ P(S \cap E) = P(E). \] Thus: \[ P(S | E) = \frac{P(S \cap E)}{P(E)} = \frac{P(E)}{P(E)} = 1. \] Step 3: Conclusion.
The conditional probability \( P(S | E) \) is: \[ \boxed{1}. \]