GATE CS 2021 Set 1 — Question 8
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Engineering Mathematics → Probability & Statistics → Elementary Statistics & Probability
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Question
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 ________
Correct answer
(C) 0.6976
Solution
Let be the number of distinct chocolates in each bag, so .
Let be the number of bags, so .
Since each bag contains the same set of distinct chocolates, picking one from each is equivalent to picking a sequence of length 5 from 10 items with replacement allowed.
Total number of outcomes = .We want the probability that at least two chocolates are identical. It is easier to calculate the complement: the probability that all chocolates are distinct.
Number of ways to pick 5 distinct chocolates from 10 types = .Probability (all distinct) = .Probability (at least two identical) = .
Let be the number of bags, so .
Since each bag contains the same set of distinct chocolates, picking one from each is equivalent to picking a sequence of length 5 from 10 items with replacement allowed.
Total number of outcomes = .We want the probability that at least two chocolates are identical. It is easier to calculate the complement: the probability that all chocolates are distinct.
Number of ways to pick 5 distinct chocolates from 10 types = .Probability (all distinct) = .Probability (at least two identical) = .
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