MATHE MATI CS 335—PRO BAB IL IT Y—SEPTEMBER 6, 2006
ASSI G NMENTS 1–2
•You should turn in your homework to the MATH 335 folder hanging outside the
Mathematics Department office, King 205, 4:30 p.m. on the due date. Solutions
will be posted to the course website shortly thereafter.
•No late homework will be accepted without a documented medical excuse. (Recall
that your two lowest homework scores will be dropped.)
•You should include details of your reasoning. Write proofs when appropriate (most
of the time!) and explain any computations you perform.
•Please be sure to label problems from the book by number and problems from this
sheet by letter. Also, please staple multiple sheets of paper together and remove
any spiral notebook scritchies.
•Please remember to write and sign the Honor Pledge, “I affirm that I have adhered
to the Honor Code in this assignment,” at the end of every problem set.
ASSIGNMENT 1. DU E MON DAY, SEPT EM BE R 11.
Durrett. Section 1.2, pages 12–13: problems 2.11, 2.15, and 2.19.
Warning: in 2.11, one of the 2+4+4’s should actually be 2+2+6.
(A) Consider 3 tetrahedral dice:
Die Ahas faces labelled 3, 5, 6, and 12.
Die Bhas faces labelled 2, 4, 9, and 11.
Die Chas faces labelled 1, 7, 8, and 10.
Let XA,XB, and XCbe the numbers on the bottom faces after dice A,B, and C
are rolled.
(a) Find Pr(XA> XB),Pr(XB> XC), and Pr(XC> XA).
(b) Consider the following game: Alice lets Bob choose one of the three dice,
A,B, or C. Knowing Bob’s choice, Alice chooses a die. Both roll, and the
higher number wins.
Should Bob be willing to play this game? Explain.
