Question

Let E and F be the events of a sample space S of an experiment, if $ P(S/F) = P(F/F) $, then $ P(S/F) $ is equal to:

• A. 0
• B. -1
• C. 1
• D. 2

Hint:

In conditional probability, when the event \( S \) is the sample space, \( P(S/F) = 1 \) since the sample space always occurs.

Answer 1

The Correct Option is C

Step 1: Understand the conditional probability. 
Conditional probability \( P(A/B) \) is defined as: \[ P(A/B) = \frac{P(A \cap B)}{P(B)}. \] In the given problem, we are given that \( P(S/F) = P(F/F) \). This represents the conditional probability of event \( S \) given event \( F \), and the conditional probability of event \( F \) given event \( F \). 
Step 2: Analyze the meaning of \( P(S/F) \) and \( P(F/F) \).
The probability \( P(S/F) \) represents the probability of event \( S \) occurring given that event \( F \) has occurred. Since \( S \) is the sample space and includes all possible outcomes, we know that: \[ P(S/F) = 1 \quad \text{(since the sample space always occurs)}. \] The probability \( P(F/F) \) represents the probability of event \( F \) occurring given that event \( F \) has occurred, which is also: \[ P(F/F) = 1. \] 
Step 3: Conclusion. 
Since \( P(S/F) = P(F/F) \) and both are equal to 1, we can conclude that the value of \( P(S/F) \) is 1. 
Final Answer: \( P(S/F) = 1 \).