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

Step 1: Understanding the Concept:
This question evaluates a specific probability calculation and the fundamental rule of complementary events.
Step 2: Key Formula or Approach:
1. Probability calculation: \(P(\text{event}) = \frac{\text{favorable}}{\text{total}}\). 2. Complementary rule: \(P(\text{not } A) = 1 - P(A)\).
Step 3: Detailed Explanation:
1. Total balls: \(5 + 2 + 3 = 10\).
2. Favorable (non-white): Red + Green = \(5 + 3 = 8\).
3. Probability (A): \(P(\text{non-white}) = \frac{8}{10} = \frac{4}{5}\). Thus, Assertion (A) is true.
4. Check Reason (R): The formula \(P(E) + P(\text{not } E) = 1\) is a standard axiom of probability. It is true.
5. Relationship: The reason provides the logical basis for calculating "non-white" (not white) as a complement to drawing a white ball.
Step 4: Final Answer:
Both Assertion and Reason are true, and Reason is the correct explanation.