A gambler goes to the casino and wins 75% of the time. How many times has he or she likely gone to the casino?

The choices were: 4 times, 100 times, It is just as likely that he has gone either 4 or 100 times

This question implies that the gambler has a system that allows him to win 75% of the time they go to the casino. Indicating he is a winning player with some sort of strategy that has that exact winrate. Thus, the answer should be either 4 or 100 are equally as likely.

For the answer of 4 times to be correct, the question should be phrased as the gambler has won 75%, which indicates luck.

Sample sizes and variance. Winning 75% on a small sample size is more likely than a larger one.

For the question about which series of lottery numbers would win with a higher probability between the 1, 2, 3, 4, 5, 6 series and the other with larger numbers, the lower digit sequence could be chosen in a lottery where the potential outcomes for each number only go up to 6, this would give this sequence a higher probability of winning than picking a sequence that would have to exist in a lottery with a greater number of permutations.

Your chance of winning or rather the degree of winning (prize share) in a lottery are potentially higher or lower when you pick your own numbers as certain sequences are picked with a higher frequency and have a smaller prize share when they win because of prize splitting.

If you flip a coin that lands heads 5 times in a row it is more likely to be an unfair/non-fair coin in the same way that if you roll a "6" on a die 5 times in a row it you are more likely to be rolling a weighted die.

Obviously all three of these are considering more angles than the more simple surface level questions and it was easy to not level myself with the smartass "correct wrong answers," but the questions should be more clearly defined to eliminate the potential misinterpretations I outlined. The first should specify the upper bound of each number chosen, the second should specify that winning any partial share of the top prize in a lottery is considered equally winning to any other partial or full share, and the third should specify that it is a "fair coin."

A gambler goes to the casino and wins 75% of the time. How many times has he or she likely gone to the casino?

The choices were: 4 times, 100 times, It is just as likely that he has gone either 4 or 100 times

This question implies that the gambler has a system that allows him to win 75% of the time they go to the casino. Indicating he is a winning player with some sort of strategy that has that exact winrate. Thus, the answer should be either 4 or 100 are equally as likely.

For the answer of 4 times to be correct, the question should be phrased as the gambler has won 75%, which indicates luck.

Sample sizes and variance. Winning 75% on a small sample size is more likely than a larger one.

I think it's also a "are you aware that all casino game odds are set in such a way that you can't win long-term" question. Overall a fun quiz but it reminds me of a driving exam where you don't need to know the material to see which answer is correct. A weekly homework question about a specific gambling situation would kinda be interesting, refresher math and probability courses would really be useful for most non-gamblers in life.