If the probability of winning a game is 0.4, the probability of losing it is
Question:

If the probability of winning a game is 0.4, the probability of losing it is
(a) 0.96

(b) $\frac{1}{0.4}$

(c) 0.6
(d) none of these

Solution:

(c) 0.6

Explanation:
Let E be the event of winning a game.
Then, ( not E) is the event of not winning the game or of losing the game.
Then, P(E) = 0.4
Now, P(E) + ​P(not E) = 1
⇒ 0.4 + ​P(not E) = 1
​⇒​ P(not E) = 1− 0.4 = 0.6
∴ P(losing the game) = ​P(not E) ​= 0.6