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You have an infinite number of chocolate candies. Two‐fifths of them have a caramel center. You choose 3 candies. What is the probability that at least 2 of them have a caramel center?

User Cnp
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1 Answer

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We can use the complement rule to solve this problem, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening.

The event we're trying to find the probability of is "at least 2 of the candies have a caramel center." The complement event is "fewer than 2 of the candies have a caramel center."

To find the probability of the complement event, we need to find the probability that exactly 0 candies have a caramel center, plus the probability that exactly 1 candy has a caramel center.

The probability that exactly 0 candies have a caramel center is (2/5)^0 * (3/5)^3 = (3/5)^3

The probability that exactly 1 candy has a caramel center is 3 * (2/5) * (3/5)^2 = (18/125)

The probability of the complement event is (3/5)^3 + (18/125)

Therefore, the probability of at least 2 of the candies having a caramel center is 1 - (3/5)^3 - (18/125)

I hope this helps :)

User Joofsh
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