In: Statistics and Probability
2.In a high school, 16% are Freshmen, 14% are Sophomores, 38% are Juniors, and 32% are Seniors. Suppose 15 students are randomly selected. Find the probability that
a) 4 are Freshmen, 5 are Sophomores, and the rest are neither Freshmen nor Sophomores (in any order)
b) either exactly one is Senior and all the others are not Senior (in any order) or exactly one Freshman, one Sophomore, one Junior and all the others are Seniors ( in any order)
Note: For each part, just give the formula as an answer; numerical answer is not required.
3. If seven fair dice are rolled, what is the probability that the number 2 and the number 6 will appear the same number of times?
(Note: “Same number of times” includes both 2 and 6 not appearing at all)