Winning the Lottery: Probability & Odds

[bartowski]

thanks for helping :)

 

[oleador]

Think about this as follows: how many ways are there to choose 2 numbers from 18? (no replacement, order doesn't matter)

 

[bartowski]

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

 

[Dickfore]

$$\frac{C^{2}_{18} \, C^{2}_{18} \, C^{2}_{19}}{C^{6}_{55}}$$

Wolfram Alpha

This looks terribly high?!

 

[bartowski]

i was thinking of that.
if you add it on the other hand, its too low

i'm not quite sure with my solution
:(

 

[Dickfore]

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.

 

[bartowski]

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? :)

 

[Dickfore]

Yes. The solution is correct.

 

[bartowski]

Yes. The solution is correct.

thanks! :)

 

[oleador]

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].

 

[bartowski]

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! :)