Probability of 0, 1, or 2 defective items in a binomial distribution

[markhboi]

can anyone help with this:

A particular type of electronic component for use in PCs is mass produced and subject to quality control checks since it is known that 5% of all components produced in this way are defective. The quality of a day's output is monitored as follows. A sample of 20 components is drawn from the day's output (which may be assumed to be large) and inspected for defective components. If this sample contains 0 or 1 defectives the day's output is accepted, otherwise it is rejected. If it contains more than 2 defectives the output is rejected. If the sample contains 2 defective a second sample of 20 is taken. If this sample contains 0 defectives the output is accepted, otherwise it is rejected.

Use the binomial distribution to calculate the probability of

(i) 0
(ii) 1
(iii) 2

defectives in a sample of 20.

Hence calculate the probability that the day's output is accepted.

Suppose that it is estimated that it costs £200 to inspect a sample of size 20. What is the expected cost of a day's sampling?

 

[VeeEight]

Go through the first part of the problem first. You know N=20. Then try n=0, 1, and 2 using what you know about calculating probabilities using binomial distribution.
It states 5% of all components are defective. So how many in a sample of 20 are defective? What is the probabilities of having 0 defectives? How about 1 and 2?
Here is a link in case: http://mathworld.wolfram.com/BinomialDistribution.html

 

[markhboi]

thats the problem, i have no clue how to do binomial and when ever i look at it online it just blags my head, anyone help me with some step by step instructions on working it out?

 

[VeeEight]

Here is a link: http://www.intmath.com/Counting-probability/12_Binomial-probability-distributions.php
It gives a description of the formula and examples, complete with solutions.

Once you have read through the page, move on to your question. It is a lot like the problems on the page. The important step is to identify the variables. Try (i) - the probably of 0 being the number of defective samples. Thus x=0. You are taking 20 total samples, so n=20. You are also given the probability that 5% are defective. Now it is a matter of plugging everything in the formula.

 

[Redbelly98]

Moderator's note: thread moved from "Set Theory, Logic, Probability, Statistics"