Bayes' Theorem and Random Variables Quiz

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Questions and Answers

What is the probability that a randomly selected student over six feet tall is a woman?

3/11 (correct)
4/13
2/5
1/5

According to the information provided, women are less likely than men to be over six feet tall.

True (A)

Define a random variable.

A random variable is a variable whose value is unknown or a function that assigns values to each of an experiment's outcomes.

The total student population is divided in the ratio ___ in favor of women.

<p>3:2</p> Signup and view all the answers

Match the following terms with their definitions:

<p>Bayes' Theorem = A mathematical formula used for finding conditional probabilities Random Variable = A variable that takes on different values based on the outcomes of a random process P(M) = Probability of selecting a male student P(F|T) = Probability that a student is female given they are over 6 feet tall</p> Signup and view all the answers

Flashcards

Bayes' Theorem

A formula for calculating conditional probability. It allows us to find the probability of an event given another event has occurred.

Conditional Probability

The probability of an event occurring given that another event has already happened.

Random Variable

A variable that takes on numerical values determined by the outcomes of a random phenomenon.

Probability of an Event given another Event

The probability of one event occurring, considering the fact that another event has already occurred.

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Study Notes

Bayes' Theorem Example

At a university, 4% of men and 1% of women are over 6 feet tall.
The student population is 3:2 in favour of women.
Probability of a randomly selected student over 6 feet tall being a woman is 3/11.

Random Variable

A random variable is a value that is unknown or a function that assigns values to experiment outcomes.

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Description

Test your understanding of Bayes' Theorem with this quiz that provides examples including the height distribution among genders in a university setting. Additionally, explore the concept of random variables and their significance in probability theory. Perfect for students studying statistics and probability.