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Questions and Answers
If 𝑃𝑟 (𝐴) = 0.3, 𝑃𝑟 (𝐵) = 0.4, and 𝑃𝑟 (𝐴 ∩ 𝐵) = 0.12, what is 𝑃𝑟 (𝐴|𝐵)?
If 𝑃𝑟 (𝐴) = 0.3, 𝑃𝑟 (𝐵) = 0.4, and 𝑃𝑟 (𝐴 ∩ 𝐵) = 0.12, what is 𝑃𝑟 (𝐴|𝐵)?
If 𝑃𝑟 (𝐴) = 0.3, 𝑃𝑟 (𝐵) = 0.4, and 𝑃𝑟 (𝐴 ∩ 𝐵) = 0.12, are events 𝐴 and 𝐵 independent?
If 𝑃𝑟 (𝐴) = 0.3, 𝑃𝑟 (𝐵) = 0.4, and 𝑃𝑟 (𝐴 ∩ 𝐵) = 0.12, are events 𝐴 and 𝐵 independent?
In the problem with 3 vendors, what is the total number of possible outcomes?
In the problem with 3 vendors, what is the total number of possible outcomes?
In the problem with 2 fair die, what is the probability of 𝐴1 ∩ 𝐴2?
In the problem with 2 fair die, what is the probability of 𝐴1 ∩ 𝐴2?
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In the problem with 10 students, what is 𝑃𝑟 (𝐴𝑐 ∩ 𝐵)?
In the problem with 10 students, what is 𝑃𝑟 (𝐴𝑐 ∩ 𝐵)?
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In the problem with 10 students, are the events 𝐴 and 𝐵 mutually exclusive?
In the problem with 10 students, are the events 𝐴 and 𝐵 mutually exclusive?
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If 𝑃𝑟 (𝐴) = 0.25 and 𝑃𝑟 (𝐵) = 0.45, what is 𝑃𝑟 (𝐴 ∪ 𝐵) if 𝑃𝑟 (𝐴 ∩ 𝐵) = 0.1?
If 𝑃𝑟 (𝐴) = 0.25 and 𝑃𝑟 (𝐵) = 0.45, what is 𝑃𝑟 (𝐴 ∪ 𝐵) if 𝑃𝑟 (𝐴 ∩ 𝐵) = 0.1?
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In the problem with 3 vendors, what is the probability that the same vendor gets both orders?
In the problem with 3 vendors, what is the probability that the same vendor gets both orders?
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Study Notes
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
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Description
This quiz covers probability concepts, including conditional probability, independence, and probability calculations. It includes two problems with multiple parts, testing understanding of probability rules and formulas.
