Probability solutions to example problems

Probability solutions to example problems - Probability...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Probability Examples (with solutions) 1. The experiment is to roll a six-sided die. (a) Write down the sample space S , that is, list all possible outcomes of this experi- ment. Solution: S = { 1 , 2 , 3 , 4 , 5 , 6 } (b) Let A be the event that die shows a number that is greater than or equal to 5. Write down the outcomes in A . Solution: A = { 5 , 6 } (c) Let B be the event that the die shows an odd number. Write down the outcomes in B Solution: B = { 1 , 3 , 5 } (d) Write down the outcome(s) in the event A B . Solution: A B = { 5 } (e) Let C be the event that the die shows a 1. Write down the outcome(s) in C . Solution: C = { 1 } (f) If all outcomes in this experiment are equally-likely, compute P ( A B ). Solution: Using the equally likely rule: P ( A B ) = num. of outcomes in A B num. of outcomes in S = 1 / 6 1 (g) If all outcomes in this experiment are equally-likely, compute P ( C B c ) Solution: Using the equally likely rule: P ( C B c ) = num. of outcomes in C B c num. of outcomes in S = num. of outcomes in num. of outcomes in S = 0 / 6 = 0 2. Suppose that for a population of 100,000 individuals: 10% of the individuals watch Hockey and Football. 35% of the individuals watch Football. 55% of the individuals watch neither Hockey nor Football. The experiment is to randomly select an individual from this population and ask about his/her football/hockey watching. Let F be the event that the randomly selected individual watches Football. Let H be the event that the randomly selected individual watches hockey. (a) Compute the probability a randomly selected individual watches either football or hockey or both, P ( F H ). Solution: In the problem statement (using the population formula), we are given that P (( F H ) c ) = 0 . 55. Using the compliment rule: P ( F H ) = 1- P (( F H ) c ) = 1- . 55 = 0 . 45 (b) Compute the probability a randomly selected individual watches hockey, P ( H ). Solution: In the problem statement (from the population formula), we are given that P ( F H ) = 0 . 10 and P ( F ) = 0 . 35, now using the union rule: P ( F H ) = P ( F ) + P ( H )- P ( F H ) solving for P ( H ) and plugging-in what we know:...
View Full Document

This note was uploaded on 05/06/2011 for the course STAT 5021 taught by Professor Staff during the Spring '08 term at Minnesota.

Page1 / 7

Probability solutions to example problems - Probability...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online