Question 443260
You start with 52 cards.  You draw a card, there is now only 51.

You now draw the second card: 

There are two cases:

You drew a black card on the first draw: Then there are only 25 blacks and 51 cards:  the probability of drawing a black: 25/51

You drew a red card on the first draw: Then there are 26 blacks still, and 51 cards:  the probability of drawing a black: 26/51

Regardless, you have drawn a card, so there are 50 cards left.

If you drew a black card and another black card, then there are 24 blacks left, 50 cards.  24/50 = 12/25

If you drew a red and black, then 25/50 = 1/2


So now we match up

Call event A: The probability of drawing three black cards is (25/51)*(24/50) = 8/34
Call event B:The probability of drawing a red, black, black is (26/51) *(25/50) = 13/51

Add these two probabilities together since either one can happen. P(A or B) = (8/34) + (13/51) = 408/1734 + 442/1734  =  {{{highlight(850/1734)}}}