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Impossible Event

Assertion A I...

Question

Assertion (A)
If the probability of winning a game is $\frac{8}{15}$ , then the probability of losing the game is $\frac{7}{15}$ .

Reason (R)
For any event E, we have P(E) + P(not E) = 1.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

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Solution

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

Explanation:
Let E be the event of winning a game.
Then, (not E) is the event of not winning the game or losing the game.
Then, P(E) = $\frac{8}{15}$
Now, P(E) + P(not E) = 1 ⇒ $\frac{8}{15}$ + P(not E) = 1
⇒P(not E) = $1 - (\frac{8}{15}) = \frac{7}{15}$
∴ P(losing the game) = P(not E) = $\frac{7}{15}$

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