Statistics

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 performs the experiments 30 times. Can the probability of drawing his favorite suit be found by using the binomial probability formula? Why or why not?

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

Can someone explain how I would solve this?

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  1. The last one:
    Yes.
    The outcomes can be classified into two categories (1-drawn card is favourite suit, 2-drawn card isn't favourite suit).
    The trials are fixed (repeating same trial over and over).
    The events are independent (the card is returned to the deck each time, so each event, or draw, doesn't depend on the previous one).

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