On her week-long trip to sunny Puerto Rico, Irvane brought 7 hats, one for each day of the week. Each case has a different color (blue, red, green, white, black, orange, purple), and thus the hats are all distinguishable. Irvane began her vacation week by choosing a permutation of the 7 hats, uniformly at random, in order to decide the order in which she will wear them throughout the week (first hat on Sunday, second on Monday, ..., seventh on Saturday). What is the probability that the first hat in this permutation is the blue one, given that the last hat in the permutation is the orange one?

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…

The 2015 Ford Mustang Fastback is available in 5 models (V6, GT, etc.) with 10 choices of color, 2 choices of transmission, and 6 types of leather interior. How many different variations of this car does Ms. Thompson have to choose from when she is buying a car?