How to Predict the Chance of Getting 12 Heads and 13 Tails from 25 Coin Tosses?

[Jamin2112]

Homework Statement

Chp 18, Rev Ex 4

A coin is tossed 25 times. Estimate the chance of getting 12 heads and 13 tails.



Chp 16, Rev Ex 8

A gambler will play roulette 50 times, betting a dollar on four joining numbers each. If one of these four numbers comes up, she gets the dollar back, together with winnings of $8. If any other number comes up, she loses the dollar. So this bet pays 8 to 1, and there are 4 chances in 38 of winning. Her net gain in 50 plays is like the sum of ____ draws from the box ____. Fill in the blanks; explain.

Homework Equations

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The Attempt at a Solution

I know how to calculate the expected value and standard error, but that can't possibly be what I use to predict an exact number such as "12 heads." Where am I supposed to go with this one? I could always just brute force it.

On the second, problem I'm confused about the phrasing "8 to 1." Does that mean she bets a dollar and has a chance of getting $9 back? If you said a bet was "2 to 1," I'd assume that meant "either you get $2 back or lose $1"; but you really wouldn't be getting $2 back because you paid a dollar to begin with. See my confusion?

 

[AdamCFC]

Isnt this maths? Have you done about probability trees? Google them

Adam

 

[Jamin2112]

Isnt this maths? Have you done about probability trees? Google them

Adam

I'm not about to do a probability tree on something with 25 repetitions

 

[Mark44]

You can approximate a binomial probability with a normal probability in this case. Your textbook should have an example of how to do this. Also, see this Wiki article, especially the section titled Binomial approximation.

 

[berkeman]

(thread moved to math sections)

 

[hgfalling]

On part 2, if a bet pays "X to 1" that means that if you win, you get your original bet back, plus X times your original bet. Gambling tables sometimes have a different designation "Y for 1" which means that your bet gets taken either way, and you get Y if you win.

So "5 to 1" and "6 for 1" are the same thing.

Unfortunately, I have no idea what is supposed to go in those blanks; maybe your textbook/class have talked about "draws from a box of something" as an equivalence for expected value or something.

 

[Jamin2112]

On part 2, if a bet pays "X to 1" that means that if you win, you get your original bet back, plus X times your original bet. Gambling tables sometimes have a different designation "Y for 1" which means that your bet gets taken either way, and you get Y if you win.

So "5 to 1" and "6 for 1" are the same thing.

Unfortunately, I have no idea what is supposed to go in those blanks; maybe your textbook/class have talked about "draws from a box of something" as an equivalence for expected value or something.

Thanks for the clarification. So there is a 4/38 chance of +$8 and a 34/38 chance of -$1. After 38 plays we expect $8 + $8 + $8 + $8 - $1 - $1 - $1 - $1 - $1 - $1 - $1 - $1 - $1 - $1 - $1 - $1 - $1 - $1 - $1 - $1 - $1 - $1 - $1 - $1 - $1 - $1 - $1 - $1 - $1 - $1 - $1 - $1 - $1 - $1 - $1 - $1 - $1 - $1 = -$2

And after a playing a ton of rounds, -$2 -$2 -$2 -$2 -$2 -$2 -$2 - ...

Money lost.