basic coin flip odds - Gambling and Probability

Two Plus Two Forums Other Topics Probability

basic coin flip odds

Post Reply Subscribe

...

10-17-2009 , 12:53 PM

smbruin22

Carpal \'Tunnel

Join Date: Aug 2005 Posts: 6,306

hi, i have a simple question. and i have done cursory check of internet with little success.

anyway, if i flip coins 100 times, what are the odds that it comes up heads over 55 times, 65 times etc??....... and i'd like to vary all the # (i.e. the 100 flips would change).

anyway, thanks in advance!

Quote

10-17-2009 , 01:50 PM

RustyBrooks

Carpal \'Tunnel

Join Date: Feb 2006 Posts: 24,647

I believe this does it
http://people.hofstra.edu/Stefan_Wan...bernoulli.html
for your case you'd do 100 trials, prob of success=0.5, P from 55 to 100

Quote

10-17-2009 , 02:05 PM

smbruin22

Carpal \'Tunnel

Join Date: Aug 2005 Posts: 6,306

rusty, thanks. couldn't get that one to work, based on my limited understanding, but it gave me the wording to google a bunch of other calculators

Quote

10-17-2009 , 03:38 PM

RustyBrooks

Carpal \'Tunnel

Join Date: Feb 2006 Posts: 24,647

OK great. I know there are a ton of them, that's just the first one that came up for me on google.

Quote

10-17-2009 , 08:21 PM

statmanhal

Pooh-Bah

Join Date: Jan 2009 Posts: 4,986

If you have Excel, you can use the BINOMDIST function.

Quote

10-19-2009 , 01:32 AM

copoka

grinder

Join Date: May 2006 Posts: 547

At least 55 - 18.41%
At least 60 - 2.84%
At least 65 - 0.18%
At least 70 - you will never see it

Quote

10-20-2009 , 09:40 AM

ivegotstylekid

adept

Join Date: Aug 2009 Posts: 781

im getting around 27% using the complement
1-(1/2)^(45/100)=.2679

Quote

10-20-2009 , 12:28 PM

spadebidder

Actually Shows Proof

Join Date: Aug 2008 Posts: 7,905

Quote:

Originally Posted by ivegotstylekid

im getting around 27% using the complement
1-(1/2)^(45/100)=.2679

I'm not really sure what you've calculated there but it isn't a binomial distribution (the chance of N successes in a series of independent win/loss trials with constant probability). copoka's answer's are correct.

Quote

10-20-2009 , 11:29 PM

ivegotstylekid

adept

Join Date: Aug 2009 Posts: 781

yea i got it (55.5-50)/5= a z score of .9 look that up on the positive z score table to get a probability to the left of .8159. subtract 1-.8159=.1814
55.5=at least 55
50=probabilty (.5) times sample 100
5 = square root of sample (100)*probability of heads(.5)*probability of tails(5)
confusing but its broken down

Quote

10-21-2009 , 07:52 PM

#10

BruceZ

Carpal \'Tunnel

Join Date: Sep 2002 Posts: 11,877

Quote:

Originally Posted by ivegotstylekid

That's the correct normal approximation, but 1 - .8149 = .1841 not .1814, and this would be correct for 55 OR GREATER which uses 54.5 instead of GREATER THAN 55 which uses 55.5. The approximation for GREATER THAN 55 comes out to about .135666. These are both excellent approximations as the exact answers (from Excel function 1-BINOMDIST) are about .18406 and .13562.

Quote

10-22-2009 , 10:53 PM

#11

smbruin22

Carpal \'Tunnel

Join Date: Aug 2005 Posts: 6,306

guys, thanks for all the help. much appreciated... and i will try the excel functions.

Quote

Post Reply Subscribe

...