flip a coin 13 times

Question

if you flip coin 13 times what is the possibility of getting exactly 9 tails 

Answer 1

Hello Eric,

 

Flipping a coin is an example of what is called a Binomial distribution.

 

When flipping a coin 13 times, the number of all possibilities is 2^13 (2 possible outcomes for each flip).

The number of ways to get exactly 9 tails from 13 flips is

(13*12*11*10*9*8*7*6*5)/(9*8*7*6*5*4*3*2*1). 

If you are familiar with factorials, the above can be written as 13!/((13-9)!9!).

3!=3*2*1. 10!=10*9*8*7*6*5*4*3*2*1. 0!=1 by definition.

 

 So, the probability of getting exactly 9 tails from 13 coin flips

= ((13*12*11*10*9*8*7*6*5)/(9*8*7*6*5*4*3*2*1))/(2^13) ≈ 0.08728.

 

The general formula for getting exactly m tails (or heads) from n flips (assuming a fair coin) is:

 

P = (n!/(m!(n-m)!))/(2^n)  (where 0≤m≤n).