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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. 0.8125
2. 0.6976
3. 0.3024
4. 0.4235

1 Answer

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Best answer
Correct Answer - Option 2 : 0.6976

Data:

To find the probability that no two chocolate are identical = P(k)

To find the probability that at least two chocolates are identical = P(x):
Formula:

P(x) = 1 - P(k)

Calculation

No two cholocate identical:

From 1st bag = Probability = \(\frac{10}{10}\)

From 2nd bag = Probability = \(\frac{9}{10}\)

From 3rd bag = Probability = \(\frac{8}{10}\)

From 4th bag = Probability = \(\frac{7}{10}\)

From 5th bag = Probability = \(\frac{6}{10}\)

P(k) = \(\frac{10 \times 9 \times 8 \times7\times6}{10\times 10 \times10 \times 10 \times10} = 0.3024\)

P(x) = 1 - P(k) = 1 - 0.3024

∴ The required result will be P(x) = 0.6976.

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