please answer b According to government data the probability

According to government data, the probability that a women between the ages of 25 and 29 was married is 40%. In a random survey of 10 women in this age group, what is the probability that Exactly 3 were married?

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 = 3 ) = ( 10 3 ) * ( 0.4^3) * ( 1 - 0.4 )^7
= 0.215
b)
P( X = 9 ) = ( 10 9 ) * ( 0.4^9) * ( 1 - 0.4 )^1
= 0.0016
P( X = 10 ) = ( 10 10 ) * ( 0.4^10) * ( 1 - 0.4 )^0
= 0.0001

P( X > = 9 ) = P( X = 9 ) + P( X = 10 ) = 0.0017

c)
Mean = np= 4
s.d = npq = 1.549