Question

Suppose two cards are drawn from a standard 52 card deck without replacement (which means when we draw a card, we don't put it back). Assuming all cards are equally likely to be selected, what is the probability that both cards are red?

Answer 1

The probability of drawing two red cards from a standard 52-card deck without replacement can be calculated using the combination formula. The probability is 0.245 or 24.5%.

Step-by-step explanation:

The probability of drawing two red cards from a standard 52-card deck without replacement can be calculated as follows:

1. First, determine the total number of ways to draw two cards from the deck, which is given by the combination formula: C(52, 2) = 52! / (2! * (52-2)!) = 1326.
2. Next, determine the number of ways to draw two red cards from the deck. Since there are 26 red cards in the deck, the number of ways to select two red cards is given by the combination formula: C(26, 2) = 26! / (2! * (26-2)!) = 325.
3. Finally, divide the number of ways to draw two red cards by the total number of ways to draw two cards to find the probability: P(both cards are red) = 325 / 1326 = 0.245.

Therefore, the probability that both cards drawn are red is approximately 0.245, or 24.5%.