{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

HW1soln

HW1soln - OR 3500/5500 Summer'08 Homework 1 Homework 1 Due...

This preview shows pages 1–2. Sign up to view the full content.

OR 3500/5500, Summer’08, Homework 1 Homework 1 Due on Tuesday, May 27, 11am. For each problem just giving the answer will not suﬃce; a proper argument is required. Problem 1 A fair die is rolled twice. (a) List the elements in the following events: A =At least one of the rolls is 6. B =The sum of the rolls is 8. C =Product of the two rolls is divisible by 6. (b) Compute P ( A ), P ( B ) and P ( C ) using the classical deﬁnition of probability. Solution (a) A = { (1 , 6) , (2 , 6) , (3 , 6) , (4 , 6) , (5 , 6) , (6 , 1) , (6 , 2) , (6 , 3) , (6 , 4) , (6 , 5) , (6 , 6) } B = { (2 , 6) , (3 , 5) , (4 , 4) , (5 , 3) , (6 , 2) } C = { (1 , 6) , (2 , 3) , (2 , 6) , (3 , 2) , (3 , 4) , (3 , 6) , (4 , 3) , (4 , 6) , (5 , 6) , (6 , 1) , (6 , 2) , (6 , 3) , (6 , 4) , (6 , 5) , (6 , 6) } (b)Sample space is: Ω = { ( i,j ) : 1 i,j 6 } Clearly #Ω = 36 and hence P ( A ) = 11 / 36 P ( B ) = 5 / 36 P ( C ) = 5 / 12 Problem 2 Prove rigorously, using the axioms and derived properties of probability

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 3

HW1soln - OR 3500/5500 Summer'08 Homework 1 Homework 1 Due...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online