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You are told that of the four cards face down on the table, two are red and two are black. If you guess all four at random, what is the probability that you get 0, 2, 4 right ?

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- Thread starter Alexsandro
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You are told that of the four cards face down on the table, two are red and two are black. If you guess all four at random, what is the probability that you get 0, 2, 4 right ?

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https://www.physicsforums.com/forumdisplay.php?f=15

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Zz.

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HallsofIvy

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What is the probability that all 4 guesses are correct? What is the probability that all 4 guesses are wrong?

The probability that exactly two of your guesses are correct is harder. If you know about "binomial probability", then this is exactly the same as aking for the probability that, if you flip a coin 4 times, it will come up heads exactly twice. Imagine writing "C" for "correct" if you guess a coin correctly, "N" for "not correct" if you guess incorrectly. The difference between this problem and the first two is that if you were guess correctly all 4 times you would write CCCC and there is only one way of doing that, if you were to guess correctly 0 times, you would write NNNN and there is only one way of doing that, but if you guess correctly exactly twice you might have written CCNN, or NNCC, or CNCN, etc. How many different ways are there of writing two C's and two N's?

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R,R B,B

R,B,B,R

R,B,R,B

B,B,R,R

B,R,B,R

B,R,R,B

B IS BLACK , R IS RED

P( o right)= 1/6

P(2 right)= 2*2/6=2/3

P(4 right)=1/6

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