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GATE 2021 BT – Question 8

General Aptitude · Quantitative Aptitude: Arithmetic and Number Computation · 2 marks · Multiple choice

Five bags contain identical sets of ten distinct chocolates. One chocolate is picked from each bag. The probability that at least two are identical is

  1. 0.3024
  2. 0.4235
  3. 0.6976
  4. 0.8125

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Correct answer: (C) 0.6976

Explanation

Each bag has the same 10 distinct chocolates, and one is picked from each of the 5 bags, so there are $10^5$ equally likely outcomes.

**Use the complement.** "At least two are identical" is the opposite of "all five are different".

**All five different:**
$$\frac{10\times9\times8\times7\times6}{10^5}=\frac{30\,240}{100\,000}=0.3024 .$$

**At least two identical:**
$$1-0.3024=\mathbf{0.6976}.$$