2 cards are drawn, w/o replacement, from 52 cards. Find the probability that one is red and one is black?

Answer 1

The answer = 1 - prob{both are red} - prob{both are black}

= 1 - [(26C2)/(52C2)] - [(26C2)/(52C2)]

= 1 - [(26!25! / 2!)/(52!51! / 2!)] - [(26!25! / 2!)/(52!51! / 2!)]

= 1 - [325/1326] - [325/1326]

= 1 - 650/1326

= 676/1326

= 26/51

Answer 2

Initially there are 26 red cards and 26 black cards, so p(red) = 1/2, and P(black) = 1/2.
If a red was drawn first, there are now 51 cards, and P(Black)= 26/51.
If a black was drawn first, there are now 51 cards, and P(red) is 26/51.
P(red then black) = 1/2 x 26/51 = 26/102 = 13/51, and
P(black then red) = 1/2 x 26/51 = 13/51.
P(one red, one black no replacement = 13/51 + 13/51 = 26/51