Probability Tutorial Problems Set 2 PDF 2024
Document Details
Uploaded by DauntlessLandArt
2024
APS
Tags
Summary
This document is a Probability Tutorial problem set for 2024. It includes problems on probability, events, set theory, and different scenarios with multiple parts (e.g.; writing outcomes), probability calculations, and determining if events are mutually exclusive or independent. Mathematics focused tutorial problems set for university or college level.
Full Transcript
Probability Tutorial problems set2- APS16W1>>2024 1. If 𝑃𝑟 (𝐴) = 0.3, 𝑃𝑟 (𝐵) = 0.4, and 𝑃𝑟 (𝐴 ∩ 𝐵) = 0.12 determine. a. 𝑃𝑟 (𝐴|𝐵) and 𝑃𝑟 (𝐴 ∩ 𝐵𝑐 ). b. Are events 𝐴 and 𝐵 independent? Justify your answer. 2. A business office orders paper supply from one of 3 vendors (𝑉1 , 𝑉2 , 𝑉3 ). Orders are pla...
Probability Tutorial problems set2- APS16W1>>2024 1. If 𝑃𝑟 (𝐴) = 0.3, 𝑃𝑟 (𝐵) = 0.4, and 𝑃𝑟 (𝐴 ∩ 𝐵) = 0.12 determine. a. 𝑃𝑟 (𝐴|𝐵) and 𝑃𝑟 (𝐴 ∩ 𝐵𝑐 ). b. Are events 𝐴 and 𝐵 independent? Justify your answer. 2. A business office orders paper supply from one of 3 vendors (𝑉1 , 𝑉2 , 𝑉3 ). Orders are placed on 2 successive days, one day per day e.g., the pair (𝑣2 , 𝑣3 ) will denote that vendor 𝑉2 gets the order on the first day and vendor 𝑉3 gets the order on the second day. a. Write down all the possible outcomes of vendors from which papers are 2 successive days. b. Let 𝐴 be the event that the same vendor gets both orders and 𝐵 the event that 𝑉2 gets at least. one order. If all the outcomes in part (a) equally likely, calculate. i. 𝑃𝑟 (𝐴) ii. 𝑃𝑟 (𝐴 ∪ 𝐵) c. Verify whether events 𝐴 and 𝐵 are mutually exclusive and independent. 3.Let A and B be two events with 𝑃𝑟 (𝐴) = 0.25 , 𝑃𝑟 (𝐵) = 0.45 and𝑃𝑟 (𝐴 ∩ 𝐵) = 0.1, what is 𝑃𝑟 (𝐴𝑐 ∩ 𝐵)? 4. Two fair die are tossed, let 𝐴1 be the event “odd number on first die”,𝐴2 be the event “odd number on second die” and 𝐴3 be the event “odd sum on both dice”. List the elements of (a) The sample spaces. (b) Events𝐴1 , 𝐴2 and 𝐴3. (c) Events 𝐴1 ∩ 𝐴2 , 𝐴1𝑐 ∩ 𝐴2 and 𝐴1 ∩ 𝐴2 ∩ 𝐴3. 5. A group of 10 students are all majoring in either Accounting or Economics or both. Five of the students are Economics majors, and seven are accounting majors. If 𝐴 denotes the event that students major in accounting and 𝐵 denotes the event that students major in Economics. a. Represent the information given above in a Venn diagram form. b. Determine the 𝑃𝑟 (𝐴), 𝑃𝑟 (𝐵), 𝑃𝑟 (𝐴𝑐 ∩ 𝐵), 𝑎𝑛𝑑 𝑃𝑟 (𝐴 ∪ 𝐵). c. Are the events 𝐴 and 𝐵 mutually exclusive? d. Determine 𝑃𝑟 (𝐴 ∪ 𝐵)𝑐 𝑎𝑛𝑑 𝑃𝑟 (𝐴 ∩ 𝐵)𝑐.
