The probability of obtaining no defective components from a

The probability of obtaining no defective components from a sample of 50 items is 0.34,
while the probability of obtaining one defective component is 0.46. What is the
probability of (a) obtaining not more than one defective component in the sample and (b)
obtaining more than one defective component in the sample?

Solution

Let X be the no of defective in the sample of 50 items

As each item is independent and also there are two outcomes only X is binomial with n =50 and p unknown

Let q =1-p

P(X=0) = q⁵⁰=0.34

P(X=1) = 0.46

a) Prob of obtaining not more than one defective component in the sample

= P(X<=1) = P(x=0)+P(x=1) = 0.34+0.46 = 0.80

b) Prob obtaining more than one defective component in the sample

= P(X>1) = 1-P(X<=1) = 1-0.80 = 0.20