Q.8 There are five bags each containing identical sets of ten distinct chocolates.
One chocolate is picked from each bag.
The probability that at least two chocolates are identical is ___________
(A) 0.3024
(B) 0.4235
(C) 0.6976
(D) 0.8125

The correct answer to this probability problem is 0.6976 (option C), calculated using the complement of all chocolates being different when picking one from each of five identical bags containing ten distinct chocolates.

Problem Breakdown

Each of the five bags holds the same set of ten unique chocolates, labeled say 1 through 10. Picking one chocolate per bag yields 10⁵ = 100,000 total possible outcomes, as each pick is independent.

The event “at least two identical” means not all five picks differ in type. Compute the complementary probability: all five different.

All Different Calculation

Probability all distinct:

• First pick any: 10/10
• Second different: 9/10
• Third: 8/10
• Fourth: 7/10
• Fifth: 6/10

P(all different) = (10 × 9 × 8 × 7 × 6) / 10⁵ = 30240/100000 = 0.3024

Thus, P(at least two identical) = 1 − 0.3024 = 0.6976.

Options Explained

• (A) 0.3024: Matches P(all different), the complement—not the target probability.
• (B) 0.4235: No direct match; possibly a miscalculation like partial permutations or incorrect complement.
• (C) 0.6976: Exact result from 1 − 0.3024, confirmed across sources.
• (D) 0.8125: Might stem from errors like assuming 1 − (9/10)⁵ ≈ 0.4095 complement or 5/10 × 5, irrelevant here.

Option Table