Question

Select each of the following experiments that are binomial experiments.

A. Drawing 3 balls without replacement from a box that contains 14 balls, 3 of which are red and 11 are blue, and observing the colors of the drawn balls.B. Selecting a few households from New York City and observing whether or not they own stocks when it is known that 20 % of all households in New York City own stocks.C. Drawing 3 balls with replacement from a box that contains 14 balls, 3 of which are red and 11 are blue, and observing the colors of the drawn balls.

Answer 1

The correct answer is B. Selecting a few households from New York City and observing whether or not they own stocks when it is known that 20 % of all households in New York City own stocks.

Explanation:

Options A and C does not fulfill the three requirements to check before calculating a binomial distribution:

• There are two mutually exclusive outcomes: "success" and "failure".
• The probability of success in a single trial is a fixed value, p.
• The result of each trial is independent of any previous trial.

In option A, each trial of drawing a ball without replacement is not independent from the previous one and in option C, the probability of success isn't a fixed value.

Therefore, the correct answer is B. Selecting a few households from New York City and observing whether or not they own stocks when it is known that 20 % of all households in New York City own stocks.

Answer 2

B. Selecting a few households from New York City and observing whether or not they own stocks when it is known that 20 % of all households in New York City own stocks.

Explanation:

For an experiment to be binomial, it needs to follow a certain number of rules. First, this experiment must have a fixed number of trials. This is because the number of trials can significantly affect your results. The second characteristic is the fact that binomial experiments require each trial to be an independent event. In other words, a trial should not have any impact on the results of subsequent trials. This allows the probability to remain constant from one trial to the next. Finally, binomial experiments should only have two possible outcomes.