Question

What is the probability that among all 100 coin flips, between 10 and 30 results in head (inclusive)?

Answer 1

Assuming the coin is a fair coin

Thus,

p = probability of getting a head = 0.5

Let X be the number of heads obtained in 100 coin flips

X ~ follows Binomial distribution with n = 100 and p = 0.5

To find

To find P(10 ≤ X ≤ 30)              
We use Excel function BINOM.DIST to find the probability              
P(10 ≤ X ≤ 30) = P(X ≤ 30) - P(X < 10)              
   = P(X ≤ 30) - P(X ≤ 9)          
   = BINOM.DIST(30, 100, 0.5, TRUE) - BINOM.DIST(9, 100, 0.5, TRUE)          
   = 0.000039          

P(among all 100 coin flips, between 10 and 30 results in head) =