Boxes numbered 1 to 10 are present at random. If a box is picked, find out the…

Correct answer: 1/2

Explanation

1. Sample space: all box numbers from 1 to 10, so n(S) = 10.

2. Multiples of 3 in this range: 3, 6, 9 (3 numbers).

3. Multiples of 5 in this range: 5, 10 (2 numbers).

4. Union of multiples of 3 or 5: 3, 5, 6, 9, 10 — total n(E) = 5.

5. Probability = n(E)/n(S) = 5/10 = 1/2

6. Therefore the correct probability is 1/2.

Notes on the other choices:

• 5/2 and 8/6 are greater than 1, so they cannot be valid probabilities.

• 5/8 is incorrect because the sample space has 10 boxes; with 5 favorable outcomes out of 10 the probability is 5/10 = 1/2.