Question

Two players, X and Y play a game of chess. The probability of X winning the game is 0.67. Find the probability of Y losing the game.

Answer 1

Hint: First, we find the probability of Y winning the game by subtracting the probability of X winning the game from 1. Then, the probability of Y losing the game can be calculated by subtracting the probability of Y winning the game from 1.

Complete step-by-step answer:
If P(A) is the probability that an event will occur, then P(A’) is the probability that the event will not occur. According to the definition of probability,
\[\text{P}\left( \text{A} \right)+\text{P}\left( \text{A }\!\!'\!\!\text{ } \right)=1\]
A’ is also called the complement of A. It can also be denoted as \[{{\text{A}}^{\text{c}}}\].
The probability of Y winning and X losing has been calculated from this definition of probability.
In this problem, P (Y wins) is the complement of P (X wins). Also, P (Y loses) is the complement of P (X loses).
Given,
P (X wins) = 0.67
The probability of Y winning the game can be calculated as:
 $ \text{P}\left( \text{Y wins} \right)=1-\text{P}\left( \text{X wins} \right) $
 $ \text{ }=1-0.67 $
 $ \text{ }=0.33 $
The probability of Y losing the game can be calculated as:
 $ \text{P}\left( \text{Y loses} \right)=1-\text{P}\left( \text{Y wins} \right) $
 $ \text{ }=1-0.33 $
 $ \text{ }=0.67 $
Therefore, the probability of Y losing the game is 0.67.

Note: Since X wins only when Y loses, the probability of X winning will be the probability of Y losing. The probability of Y losing cannot be calculated by subtracting the probability of X winning the game from 1.