What is the probability that a hand of 5 cards out of 52 is dealt all red?

Answer by  AdamSmith (14)

You start with 26 red cards, so the probability the 1st card is red is 26/52=1/2. Then the probability of being red is 25/51 for the 2nd card; 24/50(=12/25) for the 3rd card; 23/49 for the 4th card; and 22/48(=11/24) for the 5th card. So probability of all 5 cards red is: 1/2x(25/51)x(12/25)x(23/49)x(11/24)=253/9996, about 1 in 40.

Answer by  ck0689 (284)

The equation for probability is Red/Total, and because there is no replacement of the cards it is a series of the above equation. 26/52 * 25/51 * 24/50 * 23/49 * 22/48 = 7893600/311875200 = 2. 5310124%. This means that there is about a 1:50 chance of getting all red cards.