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GATE 2021 CH – Question 8

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

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 _____

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

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Correct answer: (C) 0.6976

Explanation

Use the complement: **all five chocolates are different**. There are $10^5$ equally likely selections from the five separate bags.

For an all-distinct selection the successive numbers of choices are $10,9,8,7,6$, so
$$P(\text{all distinct})=\frac{10\times9\times8\times7\times6}{10^5}=0.3024.$$

Therefore $P(\text{at least one identical pair})=1-0.3024=\mathbf{0.6976}$, **option C**.