Help with a math gambling question.?

[middle-school]

If you bet $5 that the outcome is ann odd number, the probability of losing $5 is 20/38 and the probability of making a net gain of $5 is 18/38.

If you bet $5 that the outcome is ann odd number, what is your expected value?

The answer is -.26 cents. How did they get that?

[pdq579]

****EDIT**** I typed the first half first. I like my SECOND solution down below MUCH better. Both work, but the solution near the bottom is MUCH easier to understand.

(***2nd Edit*** Yoda - WTF is that???)

********

Let's just look at what you said. 20 out of 38 chance of losing.

Into a calculator type 20 divided by 38. You get 0.52631578947368421052631578947368.

Let's simplify that to 0.526.

Multiply that times your $5.00 bet and you get 2.63. That works out to be $0.26 you will expect to lose IN THE LONG RUN if you constantly bet the 5 dollars every spin.

Of course you will never lose exactly 26 cents in any spin. You'll either LOSE 5 bucks or WIN 5 bucks. The problem is that you WILL lose more often than you'll win. ON AVERAGE, you'll win 18 times, and lose 20 times per every 38 spins.

There might be a stretch of 38 spins where you actually WIN more, but again - IN THE LONG RUN, it will work out that you will lose more.

How much more??? An average of 26 cents every time you spin that wheel.

**********

SIMPLER WAY TO THINK ABOUT IT:


Still not convinced? Do this - pretend you win exactly 18 times. That is $180. (Your 5 dollars, plus a 5 dollar profit every time you win.) Pretend you also LOST 20 times. That's $100 that you lost.

So.......out of the $180 that you WON, $90 dollars was yours. You had a 90-dollar profit.

You also LOST $100 on the 20 spins you lost.

You WON 90 dollars, but you LOST 100 dollars. That's 10 dollars lost in a total of 38 spins.

How much have you lost PER SPIN if you lost $10.00 in a total of 38 spins??? Divide $10.00 by 38. Guess what? It's 26 cents. (Actually it's 26.3 cents, but who's counting?!?)

[Ruksi]

mathemagic

[Yoda769]

****EDIT**** I typed the first half first. I like my SECOND solution down below MUCH better. Both work, but the solution near the bottom is MUCH easier to understand.

***

Let's just look at what you said. 20 out of 38 chance of losing.

Into a calculator type 20 divided by 38. You get 0.52631578947368421052631578947368.

Let's simplify that to 0.526.

Multiply that times your $5.00 bet and you get 2.63. That works out to be $0.26 you will expect to lose IN THE LONG RUN if you constantly bet the 5 dollars every spin.

Of course you will never lose exactly 26 cents in any spin. You'll either LOSE 5 bucks or WIN 5 bucks. The problem is that you WILL lose more often than you'll win. ON AVERAGE, you'll win 18 times, and lose 20 times per every 38 spins.

There might be a stretch of 38 spins where you actually WIN more, but again - IN THE LONG RUN, it will work out that you will lose more.

How much more??? An average of 26 cents every time you spin that wheel.

**********

SIMPLER WAY TO THINK ABOUT IT:


Still not convinced? Do this - pretend you win exactly 18 times. That is $180. (Your 5 dollars, plus a 5 dollar profit every time you win.) Pretend you also LOST 20 times. That's $100 that you lost.

So.......out of the $180 that you WON, $90 dollars was yours. You had a 90-dollar profit.

You also LOST $100 on the 20 spins you lost.

You WON 90 dollars, but you LOST 100 dollars. That's 10 dollars lost in a total of 38 spins.

How much have you lost PER SPIN if you lost $10.00 in a total of 38 spins??? Divide $10.00 by 38. Guess what? It's 26 cents. (Actually it's 26.3 cents, but who's counting?!?)

[LlamasThatBite294]

because theyre smart and your not dee da dee