Winning the Lottery: Probability & Odds

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Discussion Overview

The discussion revolves around the probability and odds of winning the lottery, specifically focusing on the combinatorial aspects of selecting numbers. Participants explore how to calculate the number of ways to choose numbers from a set, considering different combinations and their implications for determining probabilities.

Discussion Character

  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • Some participants propose calculating the number of ways to choose 2 numbers from 18 using combinations, specifically referencing 18C2 and 19C2.
  • There is uncertainty among participants regarding whether to add or multiply the combinations in their calculations.
  • One participant clarifies that the fraction calculated does not represent the probability of winning but rather a fraction of the total outcomes that meet certain conditions.
  • Another participant asserts that the solution presented is correct, indicating some level of agreement on the calculations.
  • Participants discuss the intuition behind multiplying combinations, suggesting that for each combination in one range, there are corresponding combinations in other ranges.

Areas of Agreement / Disagreement

While some participants agree on the correctness of the solution, there remains uncertainty about the method of combining the combinations and the interpretation of the results. The discussion does not reach a consensus on the best approach to calculating the probability.

Contextual Notes

Participants express confusion about the correct method for combining combinations and the implications of their calculations for determining winning probabilities. There are unresolved questions about the assumptions underlying their calculations.

Who May Find This Useful

Individuals interested in probability theory, combinatorics, and lottery odds may find this discussion relevant.

bartowski
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thanks for helping :)
 
Last edited:
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Think about this as follows: how many ways are there to choose 2 numbers from 18? (no replacement, order doesn't matter)
 
oleador said:
Think about this as follows: how many ways are there to choose 2 numbers from 18? (no replacement, order doesn't matter)

i was thinking about this:

numerator: 18C2, 18C2, 19C2 --- but I'm not sure if you ADD or MULTIPLY these
denominator: 55C6
 
[tex] \frac{C^{2}_{18} \, C^{2}_{18} \, C^{2}_{19}}{C^{6}_{55}}[/tex]

Wolfram Alpha

This looks terribly high?!
 
i was thinking of that.
if you add it on the other hand, its too low

i'm not quite sure with my solution
:(
 
Last edited:
No, but this not a probability ot win! This is just a fraction of the total number of outcomes that satisfy your condition. It doesn't mean that if you fill A ticket satisfying this condition that you have this probability to win.
 
Dickfore said:
No, but this not a probability ot win! This is just a fraction of the total number of outcomes that satisfy your condition. It doesn't mean that if you fill A ticket satisfying this condition that you have this probability to win.

so you think the solution is right? :)
 
Yes. The solution is correct.
 
Dickfore said:
Yes. The solution is correct.

thanks! :)
 
  • #10
The intuition for why you have to multiply the combinations is that for every possible combination, say, in [1,18] you can have 18C2 of combinations in [19,36] and 19C2 in [37,55].
 
  • #11
oleador said:
The intuition for why you have to multiply the combinations is that for every possible combination, say, in [1,18] you can have 18C2 of combinations in [19,36] and 19C2 in [37,55].

now i understand. thanks! :)
 

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