shivajikobardan Posted August 2, 2022 Share Posted August 2, 2022 An example of how probabilities are calculated in poker hand. Probability and Statistics with Applications: A Problem Solving Text By Leonard Asimow, Ph.D., ASA, Mark Maxwell, Ph.D., ASA You can ask me for more details about question, I won't paste them here, as it'd make the question too lengthy to view. What problem I'm trying to do? I am trying to find expected probability for random number independence testing aka poker test. We've 10,000 random numbers of five digit each. They're assumed to be independent. My calculations-: 1) Full house 10C1*9C1/10,000 =0.009 I'm correct. My only confusion here would be the denominator. Why is it 10,000? According to the above example, should not it be 10C5? Explanation of my thought process-: First pick 1 digit out of 10 digits. Then next, pick another digit(only 1 digit as we need a pair), out of remaining 9 digits. 2) 1 pair: Again I looked at that highlighted figure. For one pair, from 10 digits, choose 1 digit. That 1 digit makes a pair. Now you've remaining 3 choices. But none of those choices can be same to each other. So, 10C1*9C1*8C1*7C1/10,000 =0.504 I'm correct here as well. 3) 3 of a kind: Here, I need to pick only single digit for 3 places, then 2 different digits for the remaining 2 places. So, 10C1*9C1*8C1/10,000 =0.072 Here, also I'm correct. But not anymore. 4) Four of a kind: So from 10 digits, I need to pick 1 digit and out remaining 9 digits, I need to pick another 1 digit. So, it should be 10C1*9C1/10,000 But it becomes similar to full house. This is wrong. I don't get why this became wrong. 5) 5 different digits: This should've been simple, I got the answer but I got the answer greater than 1. 10C1*9C1*8C1*7C1*6C1/10,000 =3.024 I'm not sure why I got this. I am skeptical about the denominator since the start as I feel that's randomly chosen here unlike above where we did 52C5. If I increase 1 "zero" in denominator, the answer would be correct. (I've seen techniques like 10/10*9*10*8/10*7/10*6/10, but i prefer to do it as per the first poker example figure I showed so that it becomes simple for understanding). 6) Five of a kind: It should be 10C1/10,000 =0.001 but it is instead 0.0001, so it's asking for another "zero" in the denominator for correct answer. I don't know why. We have just 10,000 random numbers. This is the reason for studying this-: https://genuinenotes.com/wp-content/uploads/2020/03/Random-Numbers.pdf Link to comment Share on other sites More sharing options...
youngdan Posted January 20, 2023 Share Posted January 20, 2023 (edited) The denominator of 10,000 in your calculations is the total number of possible five-digit combinations that can be made from 10 distinct digits, which is 10^5 (10 raised to the power of 5) or 10,000. For example, in the case of a full house, you're looking for 1 pair and 3 of a kind. There are 10 possible digits for the pair, and 9 possible digits for the 3 of a kind. The probability of this outcome happening is (10C1 * 9C1) / 10,000. For 5 different digits, the probability of getting 5 different digits out of 10 possible digits is (10C1 * 9C1 * 8C1 * 7C1 * 6C1) / 10,000. For five of a kind, the probability of getting 5 of the same digit out of 10 possible digits is (10C1) / 10,000. If you're looking for a more detailed explanation I recommend checking out commercial link removed by moderator, they have a variety of resources and tutorials available that may be helpful. Edited January 20, 2023 by Phi for All No advertising, please. Link to comment Share on other sites More sharing options...
Genady Posted January 20, 2023 Share Posted January 20, 2023 5 minutes ago, youngdan said: 10^5 (10 raised to the power of 5) or 10,000. Regardless of the topic, 10^5 (10 raised to the power of 5) is 100,000 rather than 10,000. Link to comment Share on other sites More sharing options...
Recommended Posts
Create an account or sign in to comment
You need to be a member in order to leave a comment
Create an account
Sign up for a new account in our community. It's easy!
Register a new accountSign in
Already have an account? Sign in here.
Sign In Now