A diamind can be classified as either gemquality or industri

A diamind can be classified as either gem-quality or industrial-grade 80% of diamonds are classified as industrial-grade (a) Two diaminds are random. What is the probability that both diamonds are industrial-grade?

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 = 2 ) = ( 2 2 ) * ( 0.8^2) * ( 1 - 0.8 )^0
= 0.64

b)
P( X = 8 ) = ( 8 8 ) * ( 0.8^8) * ( 1 - 0.8 )^0
= 0.1678
c)

P( X < 1) = P(X=0)
= ( 8 0 ) * 0.8^0 * ( 1- 0.8 ) ^8   
= 0
P( X > = 1 ) = 1 - P( X < 1) = 1