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:

• A. 0.3024
• B. 0.4235
• C. 0.6976
• D. 0.8125

Hint:

When asked for "at least one match", always compute "no matches" first and subtract from 1.

Answer 1

The Correct Option is C

Problem understanding.
One chocolate is drawn from each of five identical bags, where each bag contains the same 10 distinct chocolates. We are required to find the probability that at least two chocolates are the same.

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Step 1: Use the complement approach.
It is easier to first calculate the probability that all five chocolates are distinct and then subtract this value from 1.

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Step 2: Compute the probability that all five chocolates are different.

• First draw: any chocolate can be chosen → probability = 1
• Second draw: must be different from the first → probability = 9/10
• Third draw: must be different from the first two → probability = 8/10
• Fourth draw: must be different from the first three → probability = 7/10
• Fifth draw: must be different from the first four → probability = 6/10

Therefore,

P(all distinct) = 1 × (9/10) × (8/10) × (7/10) × (6/10)

= 0.3024

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Step 3: Apply the complement rule.

P(at least two identical) = 1 − P(all distinct)

= 1 − 0.3024

= 0.6976

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Final Conclusion:
The probability that at least two chocolates are the same is:

Final Answer:

0.6976