Question

Assertion (A): From a bag containing 5 red balls, 2 white balls and 3 green balls, the probability of drawing a non-white ball is \(\frac{4}{5}\).
Reason (R): For any event E, \(P(E) + P(\text{not } E) = 1\)

• A. Both (A) and (R) are true and (R) is the correct explanation of (A).
• B. Both A and R are true but R is not the correct explanation of A
• C. A is true but R is false
• D. A is false but R is true.

Hint:

In "non-" or "not" questions, it's often faster to calculate the probability of the event happening and subtract it from 1.

Answer 1

The Correct Option is A

To solve this problem, we need to evaluate the Assertion (A) and Reason (R) given in the question:

1. Assertion (A): It states that the probability of drawing a non-white ball from a bag containing 5 red balls, 2 white balls, and 3 green balls is \(\frac{4}{5}\).
   • First, calculate the total number of balls in the bag: \(5 + 2 + 3 = 10\).
   • The number of non-white balls (red and green) is: \(5 + 3 = 8\).
   • Therefore, the probability of drawing a non-white ball is: \(P(\text{non-white}) = \frac{8}{10} = \frac{4}{5}\), which matches the Assertion.
2. Reason (R): It states that for any event \(E\), \(P(E) + P(\text{not } E) = 1\), which is a fundamental law of probability.
   • In the context of this problem, if \(E\) is the event of drawing a white ball, then:
     • \(P(E) = \frac{2}{10} = \frac{1}{5}\)
     • \(P(\text{non-white}) = \frac{8}{10} = \frac{4}{5}\)
     • Adding these gives: \(\frac{1}{5} + \frac{4}{5} = 1\), thereby affirming that the Reason is true.
3. Since the Reason (R) accurately explains why the Assertion (A) is true by utilizing the basic probability principle, the correct option is:

Both (A) and (R) are true and (R) is the correct explanation of (A).