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.

You are correct, the probability of drawing the favorite suit cannot be found using the binomial probability formula in this scenario. The reason is that the binomial probability formula applies when there are a fixed number of identical, independent trials each with the same probability of success.

However, in this case, the student is performing 30 trials by drawing a card from the deck and checking if it is their favorite suit. The probability of success (drawing the favorite suit) is not the same for every trial because after each draw, the card is returned to the deck and shuffled, meaning the probabilities can change with each trial.

Therefore, option (b) is the correct answer: No, the probability of success changes for every trial, so the binomial probability formula cannot be used in this case.