A shipment of 30 compressors contains 5 defectives. if we select a sample of 5 units at random for inspection: a) what is the probability that it contains exactly one defective? b) what is the probability that it contains at least one defective? c) what is the probability that it contains at least two defective?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
A shipment of 30 compressors contains 5 defectives. if we select a sample of 5 units at random for inspection:
a) what is the
b) what is the probability that it contains at least one defective?
c) what is the probability that it contains at least two defective?
a.
Let X be the number of defectives.
From the given information, there are 30 compressors. It contains 5 defectives. The sample size is 5 and probability of defective is 5/30.
Here, all the units are independent and probability of success is given. Then, X follows binomial distribution with parameters n=5 and p= 1/6.
The probability that it contains exactly one defective is
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