PSTAT W120A, Summer 2016 Assignment 1.A Due Wednesday Aug. 3 Directions: Please write up your solutions and submit them on GauchoSpace by the end of the day on Wednesday. We prefer the submission to be single pdf file if possible. Bonus points will be awarded for organization and neatness. Lesson 1 Probability Axioms 1. Use the axioms of probability to prove that for any event A, it must be that P(A) 1. 2. Let A and B be two events such that P{A B} = 0.6 and P(B) = 0.5. Calculate P{A B c }. 3. Show that for any A and B P{Ac B c } = P(Ac ) P(B) + P(AB) Lesson 2 Conditional Probability 4. If I chose a number uniformly from the integers from 1 to 25, calculate the conditional probability that the number is a multiple of 7 given that it is larger than 15. 5. There are 10 open chairs around a table. Alice and Cheryl come in and chose two seats completely at random (each seat is equally likely to be chosen but they both can't sit in the same chair.) Find the probability that Alice and Cheryl are not sitting next to each other. 6. A jar contains 12 marbles. 3 of them are red, 4 are yellow, and 5 are blue. Fred draws out a single marble at random, and then Jo draws out a second marble. (a) Given that Fred drew a red marble, what is the conditional probability that Jo got a yellow or a blue marble? (b) Given that Fred and Jo got different color marbles, calculate the conditional probability that Fred has a red marble. 1 of 1