Two cards are drawn without replacement from an ordinary deck of 52 playing cards. What are the odds against drawing two red cards?

Each of the following draws is from a set of four cards which are numbered 1,3,6,8. Two cards are drawn at random. Find the prohability that the numbers on both cards are multiples of 3? Need answer

26 to 26

OR
1 to 1

To find the odds against drawing two red cards, we first need to determine the number of favorable outcomes and the number of total outcomes.

Number of favorable outcomes:
- There are 26 red cards in a standard deck.

When we draw the first card, the probability of drawing a red card is 26/52 (as there are 26 red cards out of 52 total cards). Once the first card is drawn, there are only 25 red cards remaining out of 51 total cards.

So, the probability of drawing a second red card, given that the first card was red, is 25/51.

To find the probability of drawing two red cards in succession, we multiply these probabilities together:
(26/52) * (25/51) = 650/2652 = 325/1326

Number of total outcomes:
The number of ways to draw two cards without replacement from a deck of 52 cards is given by the combination formula C(52, 2):
C(52, 2) = (52!)/((2!)(52-2)!) = (52 * 51) / (2 * 1) = 1326

Now that we have the number of favorable outcomes (325) and the number of total outcomes (1326), we can calculate the odds against drawing two red cards:

Odds against = (Number of unfavorable outcomes) / (Number of favorable outcomes)
= (Total outcomes - Favorable outcomes) / (Favorable outcomes)
= (1326 - 325) / 325
= 1001 / 325

Therefore, the odds against drawing two red cards from a standard deck of 52 playing cards are approximately 1001 to 325.