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]
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%
