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. 0.6235 C. 0.6976 D. 0.8225

GATE 2021 · General Aptitude · Probability · medium

Answer: The probability that at least two chocolates are identical is 1 - 30240/100000 = 0.6976.

  1. Count favorable outcomes for all distinct: Favorable outcomes (all different types) = P(10, 5) = 10 * 9 * 8 * 7 * 6 = 30240.
  2. Total outcomes and P(all different): Total outcomes = 10^5 = 100000. P(all different) = 30240 / 100000 = 0.3024.
  3. Apply complement rule: P(at least two identical) = 1 - 0.3024 = 0.6976.