{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Stats213ExamSolutionsApril2011

# Stats213ExamSolutionsApril2011 - ©Prep101 Stats213 Exam...

This preview shows pages 1–6. Sign up to view the full content.

©Prep101 Stats213 Exam Solutions Solutions will be posted at www.prep101.com/solutions - 1 - II. Probability Examples 1. a) Solution: ) , 1 ( ) , 1 ( T H ) 3 , 2 ( ) 2 , 2 ( ) 1 , 2 ( ) 6 , 2 ( ) 5 , 2 ( ) 4 , 2 ( ) , 3 ( ) , 3 ( T H ) 3 , 4 ( ) 2 , 4 ( ) 1 , 4 ( ) 6 , 4 ( ) 5 , 4 ( ) 4 , 4 ( ) , 5 ( ) , 5 ( T H ) 3 , 6 ( ) 2 , 6 ( ) 1 , 6 ( ) 6 , 6 ( ) 5 , 6 ( ) 4 , 6 ( b) Solution: For each outcome where an odd appears on first toss: 12 1 ) 2 1 )( 6 1 ( = ie. P{(1,H)} = 12 1 For each outcome where an even appears on first toss: 36 1 ) 6 1 )( 6 1 ( = ie. P{(2,1)} = 36 1 c) Solution 1: Count all the possible outcomes in event A 4 1 ) 12 1 ( 3 )} , 5 ( ), , 3 ( ), , 1 {( ) ( = = = H H H P A P 2 1 ) 12 1 ( 6 )} , 5 ( ), , 5 ( ), , 3 ( ), , 3 ( ), , 1 ( ), , 1 {( ) ( = = = T H T H T H P B P Solution 2: Using conditional probability 4 1 ) 2 1 )( 6 3 ( ) | ( ) ( ) ( = = = toss first on odd Heads P toss first on odd P A P ) 2 1 ( ) ( ) ( = = toss first on odd P B P

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

View Full Document