Question

There are three cups that are turned upside down. Beneath two of the cups is a...

There are three cups that are turned upside down. Beneath two of the cups is a piece of chocolate; the last cup has nothing underneath it. You are free to choose which cup you want to turn over. What is the probability that you will first choose a cup with chocolate then, on the next choice, choose the second cup with chocolate? (After the first cup is turned over, it is not replaced.)

Math   Statistics-And-Probability   
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Answer #1

initially there are 3 cups with 2 having chocolate, probability of picking cup with chocolate :

P(chocolate) = 2/3

now there are 2 cups remaining with one having chocolate, probability of picking cup with chocolate :

P(chocolate) = 1/2

Therefore,

P(1st cup has chocolate AND 2nd cup has chocolate) = P(1st cup has chocolate)*P(2nd cup has chocolate) = 2/3 * 1/2

P(1st cup has chocolate AND 2nd cup has chocolate) = 2/6 = 1/3

P(1st cup has chocolate AND 2nd cup has chocolate) = 1/3

P.S. (please upvote if you find the answer satisfactory)

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