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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?

Guest Dec 31, 2018

#1**+1 **

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%.

Cent0rea88 Dec 31, 2018

#2**+2 **

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 = \(1-\frac{22}{425}=\frac{403}{425}\approx94.8%\)

Melody Dec 31, 2018

#3**0 **

Does that mean my answer is wrong then? Shoot. I'll have to se what I did wrong.

Cent0rea88
Dec 31, 2018

#5**+1 **

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

CPhill Dec 31, 2018