Probability Tutorial Problems Set 2
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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)?

  • 0.4
  • 0.25
  • 0.12/0.4 (correct)
  • 0.3
  • If 𝑃𝑟 (𝐴) = 0.3, 𝑃𝑟 (𝐵) = 0.4, and 𝑃𝑟 (𝐴 ∩ 𝐵) = 0.12, are events 𝐴 and 𝐵 independent?

  • Yes
  • No (correct)
  • Maybe
  • cannot be determined
  • In the problem with 3 vendors, what is the total number of possible outcomes?

  • 6
  • 9*9 (correct)
  • 9
  • 8
  • In the problem with 2 fair die, what is the probability of 𝐴1 ∩ 𝐴2?

    <p>1/4</p> Signup and view all the answers

    In the problem with 10 students, what is 𝑃𝑟 (𝐴𝑐 ∩ 𝐵)?

    <p>2/10</p> Signup and view all the answers

    In the problem with 10 students, are the events 𝐴 and 𝐵 mutually exclusive?

    <p>No</p> Signup and view all the answers

    If 𝑃𝑟 (𝐴) = 0.25 and 𝑃𝑟 (𝐵) = 0.45, what is 𝑃𝑟 (𝐴 ∪ 𝐵) if 𝑃𝑟 (𝐴 ∩ 𝐵) = 0.1?

    <p>0.6</p> Signup and view all the answers

    In the problem with 3 vendors, what is the probability that the same vendor gets both orders?

    <p>1/3</p> Signup and view all the answers

    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.

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