Homework Help: 2 quick Stats questions

1. Aug 2, 2010

Jamin2112

1. The problem statement, all variables and given/known data

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. 2. Relevant equations .... 3. 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? 2. Aug 2, 2010 AdamCFC Isnt this maths? Have you done about probability trees? Google them Adam 3. Aug 2, 2010 Jamin2112 I'm not about to do a probability tree on something with 25 repetitions 4. Aug 2, 2010 Mark44 Staff: Mentor 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. 5. Aug 2, 2010 berkeman Staff: Mentor (thread moved to math sections) 6. Aug 2, 2010 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. 7. Aug 2, 2010 Jamin2112 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.