Probability Tutorial Problems Set 2

Probability Tutorial Problems Set

Problem 1

• 𝑃𝑟 (𝐴) = 0.3 and 𝑃𝑟 (𝐵) = 0.4, with 𝑃𝑟 (𝐴 ∩ 𝐵) = 0.12
• 𝑃𝑟 (𝐴|𝐵) and 𝑃𝑟 (𝐴 ∩ 𝐵𝑐 ) need to be determined
• Events 𝐴 and 𝐵 are independent if 𝑃𝑟 (𝐴 ∩ 𝐵) = 𝑃𝑟 (𝐴) × 𝑃𝑟 (𝐵)

Problem 2

• A business office orders paper supplies from 3 vendors (𝑉1, 𝑉2, 𝑉3) on 2 successive days
• All possible outcomes of vendors from which papers are ordered on 2 successive days need to be written down
• 𝐴 is the event that the same vendor gets both orders, and 𝐵 the event that 𝑉2 gets at least one order
• 𝑃𝑟 (𝐴) and 𝑃𝑟 (𝐴 ∪ 𝐵) need to be calculated
• Events 𝐴 and 𝐵 need to be verified if they are mutually exclusive and independent

Problem 3

• Let A and B be two events with 𝑃𝑟 (𝐴) = 0.25, 𝑃𝑟 (𝐵) = 0.45, and 𝑃𝑟 (𝐴 ∩ 𝐵) = 0.1
• 𝑃𝑟 (𝐴𝑐 ∩ 𝐵) needs to be determined

Problem 4

• Two fair dice are tossed
• 𝐴1 is the event “odd number on first die”, 𝐴2 is the event “odd number on second die”, and 𝐴3 is the event “odd sum on both dice”
• Sample spaces, events 𝐴1, 𝐴2, and 𝐴3 need to be listed
• Events 𝐴1 ∩ 𝐴2, 𝐴1𝑐 ∩ 𝐴2, and 𝐴1 ∩ 𝐴2 ∩ 𝐴3 need to be determined

Problem 5

• 10 students are majoring in either Accounting or Economics or both
• 𝐴 denotes the event that students major in accounting, and 𝐵 denotes the event that students major in Economics
• Information needs to be represented in a Venn diagram form
• 𝑃𝑟 (𝐴), 𝑃𝑟 (𝐵), 𝑃𝑟 (𝐴𝑐 ∩ 𝐵), and 𝑃𝑟 (𝐴 ∪ 𝐵) need to be determined
• Events 𝐴 and 𝐵 need to be verified if they are mutually exclusive
• 𝑃𝑟 (𝐴 ∪ 𝐵)𝑐 and 𝑃𝑟 (𝐴 ∩ 𝐵)𝑐 need to be determined