Question

Determine whether the following probability experiment represents a binomial experiment and explain the reason for your answer.Sevencards are selected from a standard​ 52-card deck without replacement. The number of diamondsselected is recorded.Does the probability experiment represent a binomial​ experiment?A.​Yes, because the experiment satisfies all the criteria for a binomial experiment.B.​No, because there are more than two mutually exclusive outcomes for each trial.C.​No, because the experiment is not performed a fixed number of times.D.​No, because the trials of the experiment are not independent and the probability of success differs from trial to trial.

Answer 1

Answer:

B., C. and D.

Step-by-step explanation:

Seven cards are selected from a standard​ 52-card deck without replacement. The number of diamonds selected is recorded. Does the probability experiment represent a binomial​ experiment?

The criteria for a Binomial experiment are the following.

1. Fixed number of trials. (Not met)

The text doesn't specify the sample size (it says that seven cards are selected but doesn't specify how many times will seven cards be drawn), this number must be established before starting the experiment.

2. There are only two possible outcomes for each trial. (Not met)

"Draws seven cards and records the number of diamonds" so the outcome of the trial can be

"No diamonds"

"1 diamond card"

"2 diamond cards"

"3 diamond cards"

...

"7 diamond cards"

Simply speaking, it has two outcomes if you can phrase it as a yes or no question. That is not the case in this experiment.

3. Each trial is an independent event. (Not met)

4. The probability of success in the same from one trial to another. (Not met)

Two events are independent if the occurrence of one doesn't affect the probability of occurrence of the next one.

Since the cards are selected without replacement, at each repetition of the trial the probability of the next trial is modified. Therefore, the trials are dependant and the probability of success is modified after each trial.

None of the criteria for a Binomial experiment are met, this is not a Binomial experiment.

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