Determine the binomial distribution on five flips of a fair

. Determine the binomial distribution on five flips of a fair coin. Choose your method, but show your work. This could be done by calculating from an equation, drawing an event tree, extending from the three-flip solution or other means.

# of heads, x pr(x)

0 .......

1 ........

2 ........

3 .........

4 .........

5 .........

Solution

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

Probability of gettinng the Head in trail = 0.5
P( X = 0 ) = ( 5 0 ) * ( 0.5^0) * ( 1 - 0.5 )^5
= 0.031
P( X = 1 ) = ( 5 1 ) * ( 0.5^1) * ( 1 - 0.5 )^4
= 0.156
P( X = 2 ) = ( 5 2 ) * ( 0.5^2) * ( 1 - 0.5 )^3
= 0.313
P( X = 3 ) = ( 5 3 ) * ( 0.5^3) * ( 1 - 0.5 )^2
= 0.313
P( X = 4 ) = ( 5 4 ) * ( 0.5^4) * ( 1 - 0.5 )^1
= 0.156
P( X = 5 ) = ( 5 5 ) * ( 0.5^5) * ( 1 - 0.5 )^0
= 0.031