Well, I was in my math class (12th grade) and we are learning probabilities and statistics.

We were talking about expected value.

Here is the problem:

We have 20 balls in a bag, 4 greens, 6 orange and 10 red ones.

If we grab a green ball we get 2€ of profit, 1€ if we grab an orange and 0€ if we grab a red one.(...)
The rest of the problem doesn't really matters.

Imagine we weren't giving any money and we could grab a ball, what is the expected value?

We calculated it this way

0*(1/2)+1*(3/10)+2*(1/5)=0.7

And if we bet 1€, and we lose all we grab a red one but we get the profit from the other balls plus the amount we bet we are getting an +EV. My math teacher told me we would lose 0.3€ every time we would bet, I insinted telling we would win 0.2€ every time we bet.

Is the math correct:

-1*(1/2)+1*(3/10)+2*(1/5)=0.2 - Is it the correct way of calculating it?

try this

but looks right

Your teacher is right if I understand how the problem is written. If you are wagering 1€ for gross payoffs of €0, €1, or €2, then you spend that €1 even when you grab a orange or green ball, so your net profit on those balls is €0 and €1 respectively. EV = 0*(1/2)+1*(3/10)+2*(1/5) –1 = –0.3.

If your statement that "we get the profit from the other balls plus the amount we bet" is correct, you're right, but that seems an odd way of characterizing this bet.

Your EV is the average winnings minus the cost of the bet.

So 0.7-1=-0.3

If you want to calculate it using this form:

A*(1/2)+B*(3/10)+C*(1/5)=EV

You have to subtract one from each of the profit amounts, since it costs 1 to draw. Think about it: We win 1 when we draw a green, break even on an orange and lose 1 on a red.

So

-1*(1/2)+0*(3/10)+1*(1/5)=EV=-0.3

I mean, we get the dollar we bet back. Like if we putted it in the pot.

I think your problem is your multiplying -1 by 1/2, which you can't do since red is always zero because you can't make anything on a red draw, so it's it's always going to be -1 no matter what the prob of red is 10 or more balls so

-1 + the rest = -.3

you're teachers right. also, wrong forum

the problem is you're inventing a weird new game. in addition to the payoffs of the ball amounts, you're assigning a "win" property to the green and orange balls, meaning you get your ante back, and a "lose" property to the red balls, meaning you lose your ante. none of this is part of the original problem.