SOLUTION: Im really struggling with this problem and need help... Apply the Law of Large Numbers 1. Using a coin toss and fictitious data, explain how the following scenario is possible

Algebra ->  Algebra  -> Probability-and-statistics -> SOLUTION: Im really struggling with this problem and need help... Apply the Law of Large Numbers 1. Using a coin toss and fictitious data, explain how the following scenario is possible      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   


Question 119254: Im really struggling with this problem and need help...
Apply the Law of Large Numbers
1. Using a coin toss and fictitious data, explain how the following scenario is possible: As the number of trials increases, the differences between the number of actual and expected successes tends to grow, but the difference between the percentage of actual and expected successes tends to decrease.
Thank you..I really appreciate it..!!

Answer by scott8148(5891) About Me  (Show Source):
You can put this solution on YOUR website!
this trend is due to the increasing sample size


if you toss a fair coin 4 times, the ideal is 2 H and 2 T
___ you might get 1 of one and 3 of the other

this represents a percentage difference of 50% from the "expected" outcome
___ (2-1)/2 or (2-3)/2
___ while the actual difference is one H or T
___ this is due to the small size of the sample

toss the same coin 4000 times, and you might get 2010 H and 1990 T
___ the percentage difference from the "expected" is (2010-2000)/2000 or .5%
___ 1/100th of the small sample

at the same time, the actual difference is 10 ___ 10 times the small sample