I am a bit confused whether I should use a hypergeometric or a multinomial distribution when I encounter a questions having more than two X_i and I kinda remember that for multinomial distribution the sum of the theta for all the X_i would be equal to 1.
I have two questions as the examples while one of them is for hypergeometric and the other is for multinomial distribution.
- A quality control engineer inspects a random sample of two hand-held calculators from each incoming lot of size 18 and accepts the lot if they are both in good work- ing condition; otherwise, the entire lot is inspected with the cost charged to the vendor. What are the probabilities that such a lot will be accepted without further inspection if it contains (a) 4 calculators that are not in good working condition; (b) 8 calculators that are not in good working condition; (c) 12 calculators that are not in good working condition?
This above one is hypergeometric distribution
- The probabilities are 0.40, 0.50, and 0.10 that, in city driving, a certain kind of compact car will average less than 28 miles per gallon, from 28 to 32 miles per gallon, or more than 32 miles per gallon. Find the probability that among 10 such cars tested, 3 will average less than Special Probability Distributions 28 miles per gallon, 6 will average from 28 to 32 miles per gallon, and 1 will average more than 32 miles per gallon.
The above one is multinomial distribution.
I know they are both not in the same situations, but the two distributions have similar forms of formulas, and that was why I got confused and hope to clarify more and help myself make the right judgement.
Thank you guys in advance for any help!