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,
$$\text{P}\left(\text{A}\right)+\text{P}\left(\text{A }{}^{\prime }\right)=1$$
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:
 $\text{P}\left(\text{Y wins}\right)=1-\text{P}\left(\text{X wins}\right)$
 $=1-0.67$
 $=0.33$
The probability of Y losing the game can be calculated as:
 $\text{P}\left(\text{Y loses}\right)=1-\text{P}\left(\text{Y wins}\right)$
 $=1-0.33$
 $=0.67$
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.