Probability and Ads in TV Programs

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Questions and Answers

What is the probability of seeing ads given that the program watched is Desperate Housewives?

  • 0.2 (correct)
  • 0.15
  • 0.35
  • 0.07

What is the probability of skipping ads given that the program watched is 60 Minutes?

  • 0.015 (correct)
  • 0.1
  • 0.15
  • 0.9

Which of these options are correct? (Select all that apply)

  • The probability of watching 60 Minutes is equal to the probability of watching 60 Minutes and seeing ads plus the probability of watching 60 Minutes and skipping ads. (correct)
  • The probability of skipping ads is equal to the probability of watching 60 Minutes and skipping ads plus the probability of watching Desperate Housewives and skipping ads plus the probability of watching Football match and skipping ads. (correct)
  • The probability of seeing ads is equal to the probability of watching 60 Minutes and seeing ads plus the probability of watching Desperate Housewives and seeing ads plus the probability of watching Football match and seeing ads. (correct)
  • The probability of watching Football match is equal to the probability of watching Football match and seeing ads plus the probability of watching Football match and skipping ads. (correct)

What is the probability of seeing ads?

<p>0.455 (A)</p> Signup and view all the answers

What is the probability of watching Football match and skipping ads?

<p>0.25 (C)</p> Signup and view all the answers

What is the probability of seeing ads given that the program watched is Football match?

<p>0.5 (B)</p> Signup and view all the answers

What is the probability of Nigerian general appearing in a junk mail?

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

What is the probability that a visitor to Amazon.com made a purchase given that they came from MSN?

<p>0.552 (A)</p> Signup and view all the answers

Which of the following correctly represents the marginal probability for the event of watching 'Desperate Housewives'?

<p>P(Desperate Housewives) (C)</p> Signup and view all the answers

What does the calculation "P(Recipe Source ⋂ Purchase) / P(Purchase)" represent?

<p>The probability of a visitor making a purchase given that they came from Recipe Source. (A)</p> Signup and view all the answers

If we know that a visitor made a purchase, which of the following sources is it least likely they came from?

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

What is the most likely source of visitors who made a purchase at Amazon.com?

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

What is the probability that a visitor will watch a football match on Sunday evening?

<p>0.5 (D)</p> Signup and view all the answers

Which of the following best describes a probability tree?

<p>A graph depicting a sequence of events with conditional probabilities represented as branches. (B)</p> Signup and view all the answers

In the TV advertisement example given, what would be the probability of a viewer watching '60 Minutes' and skipping the ads?

<p>This cannot be determined from the given information. (B)</p> Signup and view all the answers

What is the approximate probability that at least two people out of 30 people will share the same birthday?

<p>70.63% (D)</p> Signup and view all the answers

According to the passage, what is the probability that no two people out of 64 people will share the same birthday?

<p>0.2810% (A)</p> Signup and view all the answers

According to the passage, what is the formula for calculating the probability of at least two people sharing the same birthday (P(A))?

<p>P(A) = 1 - P(A c) = 1 - (365 * 364 * ... * (365 - n + 1)) / 365^n (C)</p> Signup and view all the answers

According to the passage, what is the assumption that the probability calculation relies on?

<p>The probability of being born on any given day is 1/365, and each day has an equal chance of being a birthday. (B)</p> Signup and view all the answers

What does the x-axis in the graph represent?

<p>The number of people chosen at random (A)</p> Signup and view all the answers

Based on the passage, which of the following scenarios is most likely to have a probability of at least two people sharing the same birthday greater than 99.7190%?

<p>A group of 70 people (C)</p> Signup and view all the answers

What is the term used to describe the type of classification algorithm discussed in the passage?

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

According to the passage, which of the following applications is Naive Bayes commonly used for?

<p>Filtering spam emails (C)</p> Signup and view all the answers

Based on the provided information, what is the Sharpe Ratio of Disney's stock?

<p>0.0253 (D)</p> Signup and view all the answers

Which of the following accurately describes the risk-free rate?

<p>The expected rate of return on an investment with zero risk. (B)</p> Signup and view all the answers

Why is Company XYZ considered to be in financial distress?

<p>Its assets are worth less than its debt. (C)</p> Signup and view all the answers

What is the value of Company XYZ's equity if its new strategy is successful?

<p>$5 million (C)</p> Signup and view all the answers

What is the probability of failure for Company XYZ's new strategy?

<p>80% (B)</p> Signup and view all the answers

Which of the following is NOT a factor considered in the Sharpe Ratio calculation?

<p>Probability of success (C)</p> Signup and view all the answers

What is the potential downside of using the Sharpe Ratio as the sole basis for investment decisions?

<p>It only considers risk and return, not other factors like liquidity or growth potential. (A)</p> Signup and view all the answers

What is the difference between the value of Company XYZ's assets if the new strategy succeeds versus fails?

<p>$10 million (C)</p> Signup and view all the answers

What is the calculated variance for the discrete random variable X?

<p>2.917 (A)</p> Signup and view all the answers

What is the standard deviation of the discrete random variable X?

<p>1.71 (B)</p> Signup and view all the answers

In the example of the loaded die, what is the mean (μ) of the random variable X?

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

Which outcome has the highest probability in the loaded die example?

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

Which of the following calculations is used to determine variance for a discrete random variable?

<p>Var[X] = ∑(xi - μ)^2 pi (B)</p> Signup and view all the answers

If the loaded die has an extra '4', which of these numbers contributes more to the variance?

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

What is the relationship between variance and standard deviation?

<p>Variance is the square of the standard deviation. (A)</p> Signup and view all the answers

Which represents the contribution of the outcome 1 to the variance calculation in the original example?

<p>1.04167 (A)</p> Signup and view all the answers

What is the probability of rolling a sum of 2 with two dice?

<p>$\frac{1}{36}$ (C)</p> Signup and view all the answers

What is the relationship between two independent events A and B?

<p>P(A ⋂ B) = P(A) · P(B). (C)</p> Signup and view all the answers

If the probability of getting a '1' on a single die roll is $\frac{1}{6}$, what is the probability of rolling a '6' on two dice?

<p>$\frac{1}{36}$ (B)</p> Signup and view all the answers

What is the median value for the sum of two dice?

<p>7 (A)</p> Signup and view all the answers

Which of the following statements is true regarding the events of rolling two dice?

<p>Each die roll has no influence on the other die's outcome. (C)</p> Signup and view all the answers

What is the probability that the sum of two dice equals 12?

<p>$\frac{1}{36}$ (A)</p> Signup and view all the answers

Using the multiplication rule, what is the probability of rolling a '1' on the first die and a '2' on the second die?

<p>$\frac{1}{36}$ (C)</p> Signup and view all the answers

What is incorrect about the multiplication rule for independent events?

<p>It guarantees a certain outcome. (D)</p> Signup and view all the answers

Flashcards

Independence of Events

Two events A and B are independent if the outcome of A does not influence B.

Multiplication Rule

For independent events A and B, P(A ∩ B) = P(A) · P(B).

Probability of Minimum Sum (Craps)

P(Sum equals 2) = P('1' ∩ '1') = P('1') · P('1') = 1/36.

Probability of Maximum Sum (Craps)

P(Sum equals 12) = P('6' ∩ '6') = P('6') · P('6') = 1/36.

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P('1') and P('6')

The individual probabilities of rolling a '1' or '6' on a die are both 1/6.

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Event Outcomes

The possible outcomes when rolling two dice range from 2 to 12.

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Sum Equals Median (Craps)

The median value from the sum of two dice rolls is 7.

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Calculating P(A ∩ B)

To find the probability of both A and B occurring, use P(A) · P(B) for independent events.

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Conditional Probability

The probability of an event occurring given that another event has occurred.

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P(MSN Purchase)

The probability of a purchase given the source is MSN; calculated as P(MSN ∩ Purchase) / P(Purchase).

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P(Recipe Source Purchase)

The probability of a purchase given the source is Recipe Source; calculated similarly to MSN.

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P(Yahoo Purchase)

The probability of a purchase given the source is Yahoo; calculated as P(Yahoo ∩ Purchase) / P(Purchase).

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Contingency Table

A table used to display the frequency distribution of variables; often used for categorical data analysis.

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Probability Tree

A graphical representation that illustrates the probabilities of events occurring in sequence.

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Marginal Probability

The probability of an event irrespective of the outcome of other events; represented in a single dimension.

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Success of TV Advertising

The effectiveness of ads measured by viewer engagement across different TV programs.

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P(Sees Ads)

The total probability of seeing ads based on different programs.

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Joint Probability

The probability of two events happening at the same time.

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P(Skips Ads)

The probability of not seeing ads.

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Desperate Housewives Probability

The probability of watching Desperate Housewives.

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Spam Filter Example

An example of using probability to filter emails.

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P(Nigerian general appears Junk mail)

Probability of junk mail containing a specific phrase.

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P(Junk mail)

The overall probability that an email is junk mail.

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Variance (Var[X])

A measure of how data points differ from the mean in a random variable.

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Standard Deviation (SD[X])

The square root of variance, indicating average deviation from the mean.

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Mean (μ)

The average value of a random variable calculated by summing values and dividing by count.

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Probability Distribution for Loaded Die

The probabilities assigned to outcomes that reflect a loaded die scenario, favoring '4'.

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Calculation Formula for Variance

Var[X] = Σ (xi - μ)² p(xi), summing squared deviations weighted by probabilities.

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Outcome Probabilities for Loaded Die

Probability distribution: P(X=1)=1/6, P(X=2)=1/6, P(X=3)=1/6, P(X=4)=1/3, P(X=5)=1/6, P(X=6)=1/6.

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Variance of Loaded Die

The measure of spread for the outcomes of a loaded die, derived from its probability distribution.

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Calculating Standard Deviation

SD[X] is obtained by taking the square root of Variance.

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Sharpe Ratio

A measure of risk-adjusted return comparing investment performance to a risk-free rate.

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Risk-Free Interest Rate

The theoretical return on an investment with no risk of financial loss.

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Mean Return

The average expected return of an investment over time.

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Standard Deviation (SD)

A statistic that measures the dispersion of returns around the mean.

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Investment Decision (Disney vs McDonald's)

Choose the investment with the higher Sharpe Ratio for better returns.

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Expected Value with Probabilities

Calculation of outcomes based on their probabilities and potential returns.

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Financial Distress

A situation where a company cannot meet its financial obligations due to asset values.

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Probability of Success

The likelihood that a given strategy will succeed, expressed as a percentage.

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Birthday Problem

The probability that at least two people share a birthday in a group.

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Probability of Sharing Birthday with 64 People

The probability is approximately 99.72% that at least two out of 64 people share a birthday.

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Assumption in Birthday Problem

Assumes each day of the year is equally likely for a birthday.

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Complement Probability

P(A) = 1 - P(A c) where A is at least one match.

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Total Outcomes for n People

365^n possible birthday combinations for n people.

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Ways to Share Birthdays

If n people are in the room, ways at least two can share a birthday: 365 × 364 × ... × (365 - n + 1).

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Naive Bayes Classification

An effective algorithm for classifying data, based on conditional independence.

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Conditional Independence in Naive Bayes

Assumes the presence of one feature does not affect another within a class.

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Study Notes

Introduction to Probability - Decision-Making in an Uncertain World

  • Topics covered include probability theory, conditional probability, random variables (including binomial distribution), and normal distribution.
  • The long-term performance of the S&P 500 outperforms corporate and government bonds, highlighting the importance of risk and uncertainty in decision-making.
  • Business executives create value by effectively managing uncertainty.

Probability Theory

  • Random Experiment: A process leading to an uncertain outcome.
  • State Space (S): The set of all possible outcomes of a random experiment.
  • Basic Outcome: A single possible outcome in the state space.
  • Event: A subset of basic outcomes.
  • Probability: A measure of how likely an event is to occur, denoted by P(A) where A is an event. It always has a value between 0 and 1, inclusive.

Conditional Probability

  • A contingency table summarizes the counts of cases for one categorical variable contingent on the value of another; useful for calculating conditional probabilities.

Random Variables

  • A random variable is a variable whose value is subject to variation.
  • Discrete random variables take on a finite or countably infinite number of values.
  • Continuous random variables can take on (uncountably) infinite values.

Discrete Distributions

  • Probability Mass Function (PMF): A function that describes the probability of a discrete random variable.
  • Cumulative Distribution Function (CDF): Shows the probability that a random variable does not exceed a particular given value.

Normal Distribution

  • The normal distribution is a continuous probability distribution that's bell-shaped, symmetric, and centered around the mean.
  • It's characterized by two parameters: the mean (µ) and the variance (σ²).
  • The standard normal distribution is specified by a mean of 0 and variance of 1.

Student's t-Distribution

  • The Student's t-distribution is a type of continuous probability distribution. It's a symmetric and bell-shaped, similar to the normal distribution.
  • It's characterized by a parameter called 'degrees of freedom'.
  • It's important for small samples when the population standard deviation is unknown.

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