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

So what I'm thinking is that the first card doesn't matter and there is 1/2 and 1/2 for the next two cards so is the answer 1/4?

If not or If so, PLEASE GIVE EXPLANATION **WITH ANSWER**.

Guest Jul 29, 2018

#1**0 **

First calculate the probability, q, that they * are* all the same colour!

Probability that second card is same colour as first: q1 = 12/51 (12 cards of same colour to choose from out of 51 cards left).

Probability that third card is also same colour: q2 = 11/50

Hence q = q1*q2 or q = 12*11/(51*50)

Probability, p, that they are ** not** all same colour: p = 1 - q

.

Alan
Jul 29, 2018