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# math problem

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The following cards are dealt to three people at random, so that everyone gets the same number of cards. What is the probability that everyone gets a red card?

[There are three red cards and three blue cards]

Nov 29, 2022

#1
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6 / 3 = 2 - each person gets 2 cards

B = Blue,  R = Red

{BBBRRR} P 2 =4 permutations, BB,  BR,  RB,  RR - maximum number of combination that any of the 3 persons can have. I'm assuming that the 3 Blues and the 3 Reds are indistinguishable within each group of 3 cards. That is the 3 blue cards are identical and the 3 red cards are identical.

Since each person can have as many as 3 red [BR, RB, RR] combinations out of maximum number of 4 [BB, BR, RB, RR], therefore the probability of having at least 1 red is: 3/4.

Therefore, each of the other 2 persons will have the exact same probability of 3 / 4.

And the overall probability that each person has one red card is: [3 / 4]^3 = 27 / 64 =42.1875%

Nov 30, 2022
#2
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This is (at least)  the second time that this question has been posed.

The correct answer is 2/5 and two correct solutions can be found in the most recent thread, apart from this one.

Nov 30, 2022