In large lot of electric light bulbs 5% of the bulbs are defective.calculate the probability that a random sample of 20 will contain at most 2 detective bulbs

Answer 1

The outcome consists of individual answers of true/false, probability remains constant throughout, use Binomial probability.

P(n,r,p)=nCr*p^r(1-p)^(n-r)
n=size of sample
r=(exact)number of outcomes each with probability of p

At most 2 means 0,1 or 2.
The answer is P(20,0,0.05)+P(20,1,0.05)+P(20,2,0.05)

For example,
P(20,2,0.05)=20C2*0.05^2*0.95^18
=(20*19/(1*2))*0.05^2*0.95^18
=0.1887

Complete the solution by adding the two other terms.