PSTAT W120A (M18) Assignment 1.A Due Wednesday Aug. 8
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 le if possible. Make sure that your
solutions are legible, well-organized, and nished. Messy or incomplete work will be marked down.
You are encouraged to work with other students on these problems, but the actual solution must
be written individually. Bonus points will be awarded for organization and neatness.
Preliminaries
1. Read through the Syllabus and Class Guidelines links. Upload a "user picture" to your Gau-
choSpace pro le (Your head must face the camera directly with full face in view like a driver’s
license or passport photo).
Lesson 1: Probability Axioms
2. Use the axioms of probability to prove that for any event A, it must be that P(A) 1.
3. Let A and B be two events such that PfA[Bg= 0:6 and P(B) = 0:5. Calculate PfA\Bcg.
4. Show that for any A and B
PfAc\Bcg= P(Ac) P(B) + P(AB)
Lesson 2: Conditional Probability
5. If I chose a number uniformly from the integers from 1 to 25, calculate the conditional proba-
bility that the number is a multiple of 7 given that it is larger than 15.
6. 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.
7. 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 di erent color marbles, calculate the conditional probability
that Fred has a red marble.