For each situation, state whether or not a binomial distribution holds for the random variable X. Also, identify the numerical values of n and p when a binomial distribution holds.
(a) A fair die is rolled 10 times, and X denotes the number of times 6 shows up.
(b) A fair die is rolled until 6 appears, and X denotes the number of rolls.
(c) In a jar, there are ten marbles, of which four are numbered 1, three are numbered 2, two are numbered 3, and one is numbered 4. Three marbles are drawn at random, one after another and with replacement, and X denotes the count of the selected marbles that are numbered either 1 or 2.
(d) The same experiment as described in part (c), but now X denotes the sum of the numbers on the selected marbles.