Three cards are chosen at random from a standard 52-card deck. What is the probability that they are not all the same color?

The probability that the three cards are not all red (assuming that there are 26 red cards in the deck and each card is not put back in the deck after it has been drawn) is approximately 0.8824 or 88.24%.

Three cards are chosen at random from a standard 52-card deck. What is the probability that they are not all the same suite  (NOT COLOUR)?

Please note that i have answered the wrong question.  

Prob that they are all the same suite  is   \(\frac{52}{52}*\frac{\not{12}^4}{\not{51}^{17}} *\frac{11}{50} =\frac{44}{850}=\frac{22}{425}\\ \)

Prob that they are not all the same suite = \(1-\frac{22}{425}=\frac{403}{425}\approx94.8%\)

Prob that they are not the same color =  

1 - prob that they ARE all the same color

P(all the same color)  =

On the first draw, we either get a red or a black  card

The probability  that we match this on the second draw is   25 cards left of the same color / 51 cards left = 25/51

The probability that we match the color on the third draw = 24 cards left of the same color / 50 cards left

So

P( same color)  =   (1) * ( 25/51) * (24/50)  =   25/50 * 24/51  = (1/2) (8/17) =  4/17

So

P (not the same color ) =      1 - 4/17   =   13 / 17