Question

STATISTICS 30 POINTS!

A student randomly draws a card from a standard deck and checks to see if it is his favorite suit. He then returns the card to the deck, shuffles, and repeats the experiment. he performed the experiments 30 times. Can the probability of drawing his favorite suit be found by using the binomial probability formula? Why or why not?

a. Yes. The events are dependent; however, the 5% guideline can be applied to this situation.
b. No. The trials are fixed, but the probability of success changes for every trial.
c. No. The probability of success remains the same for every trial, but the trials are not fixed.
d. Yes. The outcomes can be classified into two categories, the trials are fixed, and the events are independent.

I am pretty sure it is no, but I don't know why.

Answer 1

The answer should actually be yes.

The probability of drawing a card of his favorite suit is 1/4 (there are 4 suits to from which to choose a favorite). Any card getting drawn either belongs to this suit or it does not ("can be classified into two categories").

A card is getting drawn a finite number of times ("trials are fixed").

Each time a card is drawn, it gets replaced in the deck and the deck gets shuffled, which reintroduces randomness to the card being drawn. So each draw from the deck is essentially independent from the previous draw ("the events are independent").

The answer would be D.