Quantitative Methods Week 1: Probability
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Questions and Answers

What is the probability of a randomly chosen person from the UK being under 20 years old and watching Neighbours?

  • 0.6
  • 0.4
  • 0.06
  • 0.24 (correct)

    • What is the probability of a randomly chosen person from the UK being over 20 years old?

  • 0.16
  • 0.6
  • 0.4 (correct)
  • 0.24

    • What is the probability that the lifeboat service is called out on a stormy night?

  • 0.05
  • 0.40 (correct)
  • 0.02
  • 0.10

    • What is the probability of the lifeboat service being called out on a night when the weather is not stormy?

    <p>0.10 (C)</p> Signup and view all the answers

    What is the probability of the lifeboat service being called out on a particular night, regardless of whether the weather is stormy or not?

    <p>0.05 (D)</p> Signup and view all the answers

    What is the probability that a randomly selected Accountancy graduate from the university will go into the insurance industry?

    <p>0.05 (A)</p> Signup and view all the answers

    What is the probability of getting exactly two heads when tossing three coins?

    <p>3/8 (D)</p> Signup and view all the answers

    What is the probability of selecting a female student who is studying Economics from the 1500 students?

    <p>390/1500 (B)</p> Signup and view all the answers

    What is the probability of a student selected at random being male and studying BIS?

    <p>120/1500 (C)</p> Signup and view all the answers

    How many patients are expected to stay in hospital for 2 days out of a total of 1200 patients?

    <p>350 (A)</p> Signup and view all the answers

    Given a standard deck of 52 cards, what is the probability of drawing a card that is not a heart?

    <p>3/4 (C)</p> Signup and view all the answers

    Calculate the probability of a graduate going into any type of teaching.

    <p>0.2 (C)</p> Signup and view all the answers

    What is the probability that the stock market will close higher tomorrow given the historical data?

    <p>0.06 (A)</p> Signup and view all the answers

    What is the probability that a randomly selected car loan is under £1,000?

    <p>0.054 (C)</p> Signup and view all the answers

    What is the probability that the couple will have two boys?

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

    What is the probability that a randomly selected computer purchaser is a male aged 30-44?

    <p>20/100 (D)</p> Signup and view all the answers

    What is the probability that a randomly selected CD is defective given that it was manufactured at factory A?

    <p>0.02 (D)</p> Signup and view all the answers

    What is the probability that a randomly selected outlet is in the NE region?

    <p>35/250 (D)</p> Signup and view all the answers

    What is the probability that a randomly chosen car loan was for £4,000 or more?

    <p>0.596 (D)</p> Signup and view all the answers

    If a customer is selected at random and found to be aged 30-44, what is the probability they are male?

    <p>2/5 (B)</p> Signup and view all the answers

    What is the probability of a customer being female and aged less than 30?

    <p>0.2 (A)</p> Signup and view all the answers

    What is the probability that a couple will have one of each child (boy and girl) in any order?

    <p>1/2 (B)</p> Signup and view all the answers

    Study Notes

    Quantitative Methods Week 1: Probability

    • Hospital Stays: Patients require 1, 2, or 3 days in hospital following knee surgery.

      • 700 patients stayed 1 day
      • 350 patients stayed 2 days
      • 150 patients stayed 3 days
      • Probability of needing 3 days in hospital is 150 / (700 + 350 + 150) = 0.15

    • Accountancy Graduate Destinations: Probability of different career paths after graduation.

      • Accountancy: 0.5

      • Insurance: 0.05

      • Banking: 0.05

      • Other Finance: 0.1

      • University Teaching: 0.05

      • Teaching: 0.1

      • Other: 0.15

      • Probability of a graduate going into any sort of teaching = 0.05 (University teaching) + 0.1 (Teaching) = 0.15

      • Probability a graduate does not go into accountancy = 1 - 0.5 = 0.5

    Probability of Events

    • Tossing Three Coins Possible Outcomes and Probabilities

      • Listing all outcomes:

        • HHH
        • HHT
        • HTH
        • HTT
        • THH
        • THT
        • TTH
        • TTT

      • Probability of one head: 0.375

      • Probability of two heads: 0.375

      • Probability of three heads: 0.125

    • University Students: Distributions of students based on their major and gender.

      • 1,500 total students
      • Male/Female breakdown for Accountancy, Economics, Finance, and BIS majors
      • Example calculation for probability: probability of a student being an economics major = 800/1500=0.533

    • Probability of Getting a Heart: Probability of selecting a heart card from a standard deck of 52

      • Probability of selecting a heart: 13 hearts / 52 total cards = 0.25

    • Stock Market: Describes 100 days of stock market performance.

      • 6 days risen
      • 20 days stayed the same
      • 74 days dropped

    • Loan Amounts: Distribution of car loan amounts.

      • Number of loans in different loan bracket ranges.
      • Example calculation for probability: probability of a loan being for under 1,000 = 27/500= 0.054

    • Couple's Children: Calculating probabilities for possible outcomes when a couple plans to have two children.

      • Listing possible outcomes (BB, BG, GB, GG)
      • Probability for each outcome (assuming equal likelihood for a boy and a girl)
      • Example calculation: probability of having two boys=0.25

    • Computer Purchaser Ages: Ages of computer purchasers surveyed.

      • Breakdown by age group and gender
      • Example calculation for probability: probability of a purchaser being female aged 30-44=60/200=0.3

    • Customer Age & Gender: Probability of a customer being male, given they are aged 30-44.

      • Customer age range
      • Customer gender data

    • Factory Defect Rate: Probability of a CD produced in Factory A being defective.

      • Percentage of CDs manufactured at Factory A
      • Defective rate for Factory A

    • Population by Geographic Region: Probability of selecting a fast food outlet from different geographic regions based on outlet population in the area.

    • Lifeboat Service: Probability of the lifeboat being called out given the weather conditions.

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    Related Documents

    Week 1 Probability Tutorial PDF

    Description

    This quiz covers fundamental concepts of probability as it relates to real-world scenarios, such as hospital stays post-surgery and career paths for accountancy graduates. It also explores the outcomes of tossing three coins and calculating related probabilities. Test your understanding of probability calculations and their applications.

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