There are five bags each containing identical sets of ten distinct chocolates.…
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
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Correct answer: C
Key idea: Find the probability that all five selected chocolates are different, then use the complement to get the probability that at least two are identical.
Total number of equally likely outcomes: 10^5 = 100000.
Number of outcomes with all five distinct chocolates: 10 × 9 × 8 × 7 × 6 = 30240.
Probability all five are distinct = 30240 / 100000 = 0.3024.
Therefore probability at least two are identical = 1 - 0.3024 = 0.6976 (which equals 436/625).
Answer: 0.6976
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