Question

Large Consignments of computer components are inspected for
defectives by means of a sampling system. Ten components are
examined and the lot is to be rejected if two or more are found
to be defective. If a consignments contains exactly 10%
defectives.
Find the probability of the consignment by using the technique
of Binomial probability distribution that the consignment is:
i) Accepted
ii) Rejected

Answer 1

Binomial (10,0.1)

$P(x)=\binom{n}{x}P^x(1-P)^{n-x}, x=0,1,2,...,10$

i. Probability of accepting is $P(x\le1)$

$P(x\le1)=P(x=0)+P(x=1)$

$=[\binom{10}{0}\times(1-0.1)^{10}]+[\binom{10}{1}\times0.1^1(1-0.1)^9]$

$=0.349+0.387$

$=0.736$

ii. Probability of rejecting is $P(x>1)$

$P(x>1)$ is 1- probability of accepting

$P(x>1)=1-P(x\le1)$

$=1-0.736$

$=0.264$