In a group of 20 ballpoint pens on a shelf in the stationery

In a group of 20 ballpoint pens on a shelf in the stationery department of Metro Department Store, 2 are known to be defective. If a customer selects 3 of these pens, what is the probability that:

a. At least 1 is defective

b. No more than 1 is defective

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 > = 1 ) = 1 - P( X < 1) = 0.271
P( X < 1) = P(X=0)   
= ( 3 0 ) * 0.1^0 * ( 1- 0.1 ) ^3 +
= 0.729
b)
P( X < = 1) = P(X=1) + P(X=0)
= ( 3 1 ) * 0.1^1 * ( 1- 0.1 ) ^2 + ( 3 0 ) * 0.1^0 * ( 1- 0.1 ) ^3
= 0.972