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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.

Respuesta :

Answer:

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.

Following are the response to the given points:

The binomial experiment includes the following conditions that must be fulfilled:

  • There will only be two outcomes, which are usually labeled as "successes" and "fails".
  • Its chances of success (and thus failure) must be equal throughout all trials, implying that the result of each test has to be autonomous of the outcomes of earlier trials.
  • This experiment's number of tests must be fixed.
  • Since each ball is replaced after the draw, the trials are independent, the probability of success is consistent, and the number of tests is constant, this is a binomial distribution (here, 3).
  • Since the trials are not independent, it is not a binomial test (sampling without replacement).
  • Binomial experiment if all of the preceding requirements are fulfilled.

Learn more:

brainly.com/question/15395370

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