Problem 1. A bag of marbles contains 12 blue, 7 green, and 3 white marbles. You randomly choose 3 marbles at random (without replacement). Make sure to show your fraction first, then convert all fractions to a percent or decimal number. Find the following probabilities: a) All three are blue marbles. b) First one is blue, the second is white, and the third is white. c) At least one is green.

Problem 2. A local elementary school conducted their own independent survey by randomly selecting their students and staff and asking them what their favorite ice cream flavor is. The result of the survey is listed below. Write out your fractions first, then convert them to either a decimal or percentage number. Vanilla Chocolate Lemon Strawberry Total Student 80 50 32 40 202 Staff 70 42 50 60 222 Total 150 92 82 100 424 If we choose one person at random, find the following probabilities: a) The person is a staff and likes Lemon. b) The person likes Vanilla given the person is a student. c) The person likes Strawberry or is a student.

Problem 3. In Los Angeles County, the length of a criminal trial is known to be normally distributed with a mean of 44.8 days and a standard deviation of 6.3 days. Include your normal curve for all parts and shade the area! a) If one of the trials is randomly chosen, find the probability that it lasts more than 36 days. [4 pts] b) Find the 55th percentile of criminal trials. c) If 27 criminal trials are randomly selected, find the probability that they will last between 40 and 42 days.