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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
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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
 #2
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Alan seems to be using a pack where each suit has its own colour !

Guest Jul 29, 2018
 #3
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Oops! You are right!

 

I should have q1 =  25/51 and q2 = 24/50.

Alan  Jul 29, 2018

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