A packet of 10 electronic components is known to include 2 defectives. If a sample of 4
components is selected at random from the packet, what is the probability that the sample
does not contain more than 1 defective?
Answers
The probability that the sample does not contain more than 1 defective is 0.8192.
Step-by-step explanation:
We are given that a packet of 10 electronic components is known to include 2 defectives.
Also, a sample of 4 components is selected at random from the packet.
The above situation can be represented through Binomial distribution;
where, n = number of trials (samples) taken = 4 electric components
r = number of success = not more than 1 defective
p = probability of success which in our question is probability that
electric components are defective, i.e; (2÷10) = 0.20 or 20%
LET X = Number of electric components that are defective
SO, X ~ Binom(n = 4, p = 0.20)
Now, probability that the sample does not contain more than 1 defective is given by = P(X 1)
P(X 1) = P(X = 0) + P(X = 1)
=
=
= 0.4096 + 0.4096
= 0.8192
Therefore, probability that the sample does not contain more than 1 defective is 0.8192.