A manufacturer of DVD players receives a shipment of 50 capa

A manufacturer of DVD players receives a shipment of 50 capacitors, 3 of which are defective. To determine if they will accept the shipment, they randomly select 10 capacitors and test each. If there is more than one defective transistor in the sample, they will reject the entire shipment. Find the probability that the shipment is rejected.

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

P( X < = 1) = P(X=1) + P(X=0) +   
= ( 10 1 ) * 0.06^1 * ( 1- 0.06 ) ^9 + ( 10 0 ) * 0.06^0 * ( 1- 0.06 ) ^10 +
= 0.88241
P( X > 1) = 1 - P ( X <=1) = 1 -0.88241 = 0.11759