What is chance of obtaining 5 heads and 15 tails when we tos

What is chance of obtaining 5 heads and 15 tails when we toss a fair coin 20 times? Answer should be simplified fraction a/b. Hint: The answer can be found using n =20 in pascal triangle or using binomial expansion of (1/2 + 1/2)²⁰.

Solution

P(5 H , 15 T) :

We toss 20 times
Let the success be getting head...
So, x = 5

n = 20(total number of trials)

p = probability of success = probability of head = 1/2

1 - p = probability of failure = probability of tail = 1 - 1/2 = 1/2

USing binomial formula, which is :

P(x) = (n C x) * p^x * (1 - p)^(n - x)

We get :

P(5 heads , 15 tails) = (20 C 5) * (1/2)^5 * (1/2)^15

15504 * (1/2)^20

15504 / 2^20 -----> ANSWER