Let \( E \) be an event of a sample space \( S \) of an experiment, then \( P(S | E) \) is:
Show Hint
- \( P(S \cap E) \)
- \( P(E) \)
- \( 1 \)
- \( 0 \)
The Correct Option is C
Solution and Explanation
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: \[ \boxed{1}. \]
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