Select each of the following experiments that are binomial experiments:

a) Drawing 3 balls without replacement from a box that contains 10 balls, 4 of which are red and 6 are blue and observing the colors of the drawn balls.
b) Drawing 3 balls with replacement from a box that contains 10 balls, 4 of which are red and 6 are blue and observing the colors of the drawn balls.
c) Selecting a few households from New York City and observing whether or not they own stocks when it is known that 40 % of all households in New York City own stocks.

a) No.

b) Yes.

c) Yes.

Step-by-step explanation:

a) No.

As being without replacement, the probabilities of each color in each draw change depending on the previous draws.

This is best modeled by an hypergeometric distribution.

b) Yes.

As being with replacement, the probabilities for each color is constant.

Also, there are only two colors, so the "success", with probability p, can be associated with the color red, and the "failure", with probability (1-p), with the color blue, for example.

(With more than two colors, it should be "red" and "not red", allowing only two possibilities).

c) Yes.

The answer is binary (Yes or No) and the probabilities are constant, so it can be represented as a binomial experiment.

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