Question

If probability of winning a game is \(p\), then probability of losing the game is:

• A. \(1 + p\)
• B. \(-p\)
• C. \(p - 1\)
• D. \(1 - p\)

Answer 1

The Correct Option is D

Problem:
We are told that the probability of winning a game is \( p \). We are to determine the probability of losing the game.

Step 1: Understand the total probability of all outcomes
In probability theory, the sum of probabilities of all mutually exclusive outcomes of an event is always equal to 1.
That is:
\[ \text{Probability of winning} + \text{Probability of losing} = 1 \]

Step 2: Use given information
Given that the probability of winning = \( p \), we can substitute into the total equation:
\[ p + \text{Probability of losing} = 1 \Rightarrow \text{Probability of losing} = 1 - p \]

Final Answer:
The probability of losing the game is \(1 - p\).