What is the probability of drawing three red cards, one at a time without replacement, from a standard deck of 52 cards?
.11764?
2/17=.11764
To calculate the probability of drawing three red cards, one at a time without replacement, from a standard deck of 52 cards, we need to determine the total number of ways we can draw three cards and the number of successful outcomes.
The total number of ways to draw three cards is given by the combination formula:
C(n, k) = n! / (k!(n-k)!)
Where n is the total number of cards (52) and k is the number of cards we want to draw (3).
C(52, 3) = 52! / (3!(52-3)!) = 22,100
Next, we need to determine the number of successful outcomes, which in this case is selecting three red cards.
There are 26 red cards in a standard deck, so the first card has a 26/52 (or 1/2) chance of being red. After that, there are 25 red cards remaining out of 51 total cards, so the second card has a 25/51 chance of being red. Similarly, the third card has a 24/50 chance.
Therefore, the probability of drawing three red cards, one at a time without replacement, from a standard deck of 52 cards is:
(26/52) * (25/51) * (24/50) = 0.0588 or 5.88%
consider how many reds and the total cards there are for each draw. You multiply the chances for each event, giving
26/52 * 25/51 * 24/50