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.