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GATE | GATE CS 2021 | Set 1 | Question 8

  • Last Updated : 24 May, 2021

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


Answer: (C)

Explanation: Bags are identical but not chocolates. Chocolates are distinct.

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We picked one chocolates from each bag. Order does not matter here.

The probability that at least two chocolates are identical
= 1 – (all are distinct chocolates)
= 1 – (10/10*9/10*8/10*7/10*6/10)
= 1 – 30240 / 100000
= 69760 / 100000
= 0.6976

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