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?
<em><u>The criteria for a Binomial experiment are the following.</u></em>
<em><u /></em>
<em>1. Fixed number of trials. </em>(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.
<em>2. There are only two possible outcomes for each trial.</em> (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.
<em>3. Each trial is an independent event.</em> (Not met)
<em>4. The probability of success in the same from one trial to another.</em> (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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