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

Flashcards

Probability of 3 Days in Hospital

The likelihood of needing to stay 3 days in the hospital after surgery.

Probability of Teaching Careers

The chance that an accountancy graduate chooses any teaching role.

Not Going into Accountancy

The probability that an accountancy graduate does not choose accountancy as a career.

Coin Toss Outcomes

All the different results that can occur from tossing three coins.

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Probability of Male Student

The likelihood that a randomly selected student from a class is male.

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Probability of Economics Degree

The chance that a randomly selected student is studying economics.

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Probability of Heart in Card Deck

The likelihood of drawing a heart from a standard deck of cards.

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Probability of Outlet in NE

The likelihood that an outlet is located in the Northeast given a large population area.

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Independent Events

Two events are independent if the occurrence of one does not affect the other.

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Probability under 20 & Watches Neighbours

The joint probability that a randomly selected UK individual is under 20 and watches 'Neighbours'.

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Probability of Going to Film and Bar

The likelihood that a student goes to a film and then to the bar on a night out.

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Addition Rule of Probability

The formula for finding the probability of either of two events occurring.

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Probability of market rise

The likelihood of the stock market closing above 2721 based on past performance.

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Loan probability under £1,000

The chance of randomly selecting a loan under £1,000 from 500 total loans.

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Loan probability £4,000 or more

The chance of randomly selecting a loan that is £4,000 or greater.

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Child gender outcomes

The potential combinations of genders for two children: boy-boy, boy-girl, girl-boy, girl-girl.

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Probability of two boys

The chance of having two boys in two births, assuming equal likelihood.

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Male customer probability (30-44)

The likelihood that a randomly selected customer aged 30-44 is male.

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Defective CD probability from factory A

The chance that a CD is defective given it was produced at factory A.

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Outlet selection probability in NE

The probability of randomly selecting a fast-food outlet located in the Northeast region.

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Total loan breakdown

The classification of 500 loans into specific monetary ranges.

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Combined population of fast-food outlets

Understanding the distribution of fast-food outlets by population size and geographic region.

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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

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