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

Step 1: Understanding the problem:
We are given that the probability of winning a game is \( p \), and we need to find the probability of losing the game.

Step 2: Relationship between winning and losing probabilities:
The sum of the probabilities of all possible outcomes of an event must always be 1. In this case, the two possible outcomes are winning and losing the game.
Therefore, the probability of losing the game is the complement of the probability of winning the game.
This can be expressed as:
\[ \text{Probability of losing} = 1 - \text{Probability of winning} \] Substituting \( p \) for the probability of winning:
\[ \text{Probability of losing} = 1 - p \]

Step 3: Conclusion:
The probability of losing the game is \( 1 - p \).