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Each packet of a certain cereal contains a small plastic model of one of five different dinosaurs; a
packet is equally likely to contain any one of the five dinosaurs. Find the probability that someone
buying six packets of the cereal will acquire models of their three favourite dinosaurs. Using inclusion and exclusion probability
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In this problem, we have random samples of 6 items from an unlimited pool of items of 5 different types mixed evenly.
Selection an item of one or another type at each trial is random; each type can be selected with the probability 1/5.
For us, the success at each random trial is to get randomly any item of some of 3 favorite types;
so, the probability of success is 3/5 at each individual trial.
The number of trials is 6.
Thus, we have a Binomial distribution experiment with 6 trials, 3 success trials
and probability of the individual success at each trial of 3/5.
Hence, to answer the question, use the standard formula of partial binomial distribution probability
P = = = 0.27648 (rounded).
ANSWER.
Solved.
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The last instruction in this post "Using inclusion and exclusion probability" is IRRELEVANT and does not make any sense.
These terms are never used in this area, so do not try to invent, to introduce and to use them. It is not a good style.