Geometric Random Variable

[Agent Smith]

If the probability of winning the lottery is \(\displaystyle p\) then the number of trials (the number of times you'll have to purchase the lottery) until a WIN = \(\displaystyle \frac{1}{p}\).

Is WIN here:

1. Around 1 WIN
2. At least 1 WIN
3. At most 1 WIN
3. Exactly 1 WIN

?

 

[Dr.Peterson]

If the probability of winning the lottery is \(\displaystyle p\) then the number of trials (the number of times you'll have to purchase the lottery) until a WIN = \(\displaystyle \frac{1}{p}\).

Is WIN here:

1. Around 1 WIN
2. At least 1 WIN
3. At most 1 WIN
3. Exactly 1 WIN

?

It's a poorly worded statement.

It could mean, "what is the expected number of trials until the first win". But it doesn't quite say that.

If you're asking, what is the question that has that answer, then what I just said is correct:

Number of Trials to First Success

www.cut-the-knot.org

I found that (among many others) by searching for "expected number of trials until success".

Note that your question is inadequate, since it isn't primarily just a matter of what "win" means, and none of your choices is correct.

 

[Agent Smith]

expected number of trials until the first win

Cogito, this is the answer. So if a game has a probability of win = 1/3 and you played this game repeatedly, the mean of the number of times you had to play to win 1 time = 3. Yes?

E(number of trials until success/win).