Probability

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jshaziza

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When playing five card poker, a royal flush consists of a 5-card hand with A-K-Q-J-10 of the same suit.
a.How many royal flushes are there? (order is not important)

b. What is the probability of getting a royal flush?

Originally for these two questions I had for b. 1/13 because there are 4 different sets out of 52 cards and for a. I had 4 as my answer. But then I thought about what they said when they mentioned order is not important, and I figured I probably had to use nCr formula to solve so for n I put 20 and for r I put 5. The reason for those two numbers was that there are 5 cards in a flush and 20 different cards that can be combined to make a flush.

So did I do that correctly? And fif so does my answer for b. change at all? Thx. for your help.
 
You got the odds of getting a royal flush as 1 in 13?

Are you ready? The odds are 1 in 649,740 :shock:

Are you a student with teacher/classroom, or learning on your own?
 
jshaziza said:
When playing five card poker, a royal flush consists of a 5-card hand with A-K-Q-J-10 of the same suit.
a.How many royal flushes are there? (order is not important)

b. What is the probability of getting a royal flush?

Originally for these two questions I had for b. 1/13 because there are 4 different sets out of 52 cards and for a. I had 4 as my answer. But then I thought about what they said when they mentioned order is not important, and I figured I probably had to use nCr formula to solve so for n I put 20 and for r I put 5. The reason for those two numbers was that there are 5 cards in a flush and 20 different cards that can be combined to make a flush.

So did I do that correctly? And fif so does my answer for b. change at all? Thx. for your help.
Click to expand...

Your answer to part (a) is correct. There are just 4 possible royal flushes, one in each of the four suits.

For part (b),

P(royal flush) = (number of royal flushes) / (number of possible 5-card hands)

To find the number of possible 5-card hands, you'll need to compute the number of combinations (since order is not important) of 52 cards taken 5 at a time.

P(royal flush) = 4 / ( 52 C 5)

I'll leave the calculation to you.
 
Just from another angle: You can choose any of A,K,Q,J,10 in any suit. Thats 20/52.

Then each of the next 4 cards have to be the the same suit as the first we picked and there are four cards we need to get. So the probabilities are 4/51, 3/50. 2/49, 1/48.

Using the law of conditional probability (the next four were chosen given we have a specific suit now), thats (20*4*3*2*1)/(52*51*50*49*48) = 1/649740.

I actually had one in a holdem' game about 6 months ago. I didn't win much money... I'm an easy read apparently :(.
 
Thx. you guys for your help. And Dennis, yes I am learning on my own right now, I live in Alaska for the time being and I don't live near a school, so I am under a program called CSS-correspondance study school, believe it or not all these questions I am asking right now are questions that I wasn't able to get from 18 lessons of Algebra 2, with 20-40 questions each, so considering, I am doing pretty good. I am not trying to brag or anything, it's just not easy having to teach yourself 6 different subjects, and sometimes I get confused or stuck and need your guy's help, so please have patience with me. I only have a couple more questions and then I can send off my Math. Thx. again I really appreciate it, you guys are life savers! :D
 
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