Half Betting

How do you work out odds in a deck of cards?

If you want to know the odds of pulling out certain cards and have a certain number of attempts what is the formula for working these out? Example: If I already know 5 cards are missing from the 52 card deck, these cards are - 7h, 8d, 2c, 9d, 10s I want to work out the odds of being about to draw out any J or 6 (8 of these options remaining in the deck) and I have two attempts to do it What would be the formula and the odds on being able to do this?

Public Comments

1. odds would be 8 out of 47 the first time and then depending on if you drew one of not if you did: 7 out of 46 if you didnt: 8 out of 46
2. There are 4 jacks and 4 6's left in a deck of 47. Therefore, the odds of drawing a jack or a 6 in the first draw are (4+4)/47 = 8/47. If you drew a jack or a 6 in the first draw, the odds of drawing one in the 2nd draw are 7/46. If not, the odds are 4/23.
3. 52 to 1
4. actually you can consider the first answer but you said odds and its defined as no of favorable outscomes over no. of unfavorable outcomes so at first: its 8/39 if you got one of them obviously you stop since you got one if not its odd is 8/38 in probability you add them 8/47+39/47*8/46 which is .3145 31.45% that is a big chance try it out 12 times you probably get it in 3 or 4 of your tries....
5. I assume that you meet your objective if you draw a J or 6 on both draws as well. The easiest way to do this is calculate the chance of not drawing a J or six on the two draws then subtract this from one. So the probability is 1-39/47*38/46 = 0.31452(5dp).