Suppose that a course has 3 sections with 50, 70, and 80 students. Let's say we randomly pick one of the 3 sections, and give all of their students a spooky costume. What's the expected number of costumes we'd give out?

Suppose I gave you a bag of M&M’s, but I didn’t let you see the original packaging so you can’t determine which plant made the M& M’s.  Your job is to count the number of candies of each color in your bag and figure out which plant made your bag.  What test should you do to determine this?

A shoe company wants to test an updated model of a running shoe on its wear after one month of running. Which of the following describes a matched pairs design? They recruit 50 people who run on a regular basis to participate in their study. They will have the runners wear the shoes when they run for two months. After two O The subjects are numbered 1-50, and these numbers are put into a random number generator. The first 25 random numbers, ignoring repeats, represent the subjects assigned to the new model group. The remaining 25 subjects will wear the original model. months, the wear on the shoes will be determined using the depth of the tread and flexibility of the toe box. The wear between the new model and the original model will then be compared. The subjects' names are written on equal-sized slips of paper and placed into a hat. A researcher then reaches in and pulls out 25 slips of paper. These subjects are assigned to the new model group. The remaining 25 subjects will be…

I have a cup with 5 red M&Ms, 4 yellow, and 3 green ones. I draw six at random (without replacement, order does not matter).How many ways are there to draw six at random which give two of each color? For this problem, it can help to imagine that the M&Ms are numbered 1 - 12, with number 1-5 red, 6-9 yellow, and 10-12 green. After that, proceed like we did with Poker hands.

A person, Joe, claims to be able to "smell" an illness based on the odor of a person's clothing. Joe is given 12 shirts, each worn by a different person, some of whom had the illness and some of whom did not. The shirts were given to Joe in random order and he had to decide whether each shirt had been worn by an ill patient or by a healthy patient.  joe identified 11 of the 12 shirts correctly. If we assume that Joe was just guessing, he would have probability 1/2 of correctly identifying each shirt.  Find the probability that Joe would identify AT LEAST 11 shirts correctly by random guessing

A teacher will randomly award three students with extra credit. How many possible ways can the teacher pick these three students from a class of 20 students?