A certain drug treatment cures 90 of cases of hookworm in ch

A certain drug treatment cures 90% of cases of hookworm in children. Suppose that 20 children suffering from hookworm are to be treated, and that the children can be regarded as a random sample from the population. Find the probability that

All 20 will be cured

All but 1 will be cured

Exactly 18 will be cured

Exactly 90% will be cured

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

a)
P( X = 20 ) = ( 20 20 ) * ( 0.9^20) * ( 1 - 0.9 )^0
= 0.1216
b)
P( X = 19 ) = ( 20 19 ) * ( 0.9^19) * ( 1 - 0.9 )^1
= 0.2702

c)
P( X = 18 ) = ( 20 18 ) * ( 0.9^18) * ( 1 - 0.9 )^2
= 0.2852
d)
it is same as c, 90% of 20 = 18 will be cured