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Probability Distributions. Problem: Suppose you are taking a true or false test with 6 questions…. But you didn’t study at all. Take out a coin and a piece of paper – you will flip your coin to answer the following problems. Heads is true, tails is false. STATISTICS 257 Final Exam – Oh no!.

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Problem suppose you are taking a true or false test with 6 questions but you didn t study at all
Problem: Suppose you are taking a true or false test with 6 questions…. But you didn’t study at all

  • Take out a coin and a piece of paper – you will flip your coin to answer the following problems.

  • Heads is true, tails is false.


Statistics 257 final exam oh no
STATISTICS 257 Final Exam – questions…. But you didn’t study at allOh no!

Get out your coin and guess the following:

1. If a gambling game is played with expected value 0.40, then there is a 40% chance of winning.


I lost my notebook
… I lost my notebook… questions…. But you didn’t study at all

  • 2. If A and B are independent events and P(A)=0.37, then P(A|B)= 0.37.


The textbook is too heavy
…the textbook is too heavy questions…. But you didn’t study at all

  • 3. If A and B are events then P(A) + P(B) cannot be greater than 1.


I m never going to really need this stuff anyway right
... I’m never going to really need this stuff anyway, right?

  • 4. If P(A and B) = 0.60, then P(A) cannot be equal to 0.40.


Why are the questions so long
…why are the questions so long? right?

  • 5. If a business owner, who is only interested in the bottom line, computes the expected value for the profit made in bidding on a project to be -3,000, then this owner should not bid on this project.


Oops i left my calculator in my locker
…. Oops, I left my calculator in my locker right?

  • 6. Out of a population of 1000 people, 600 are female. Of the 600 females 200 are over 50 years old. If F is the event of being female and A is the event of being over 50 years old, then P(A|F) is the probability that a randomly selected person is a female who is over 50.


So how did you do
So how did you do? right?

  • #1 – False

  • #2 – True

  • #3 – False

  • #4 – True

  • #5 – True

  • #6 – False

    Tally up your responses – Did you pass?


The distribution of scores on the test why is it more likely to get 3 right than to get 6 right
The Distribution of scores on the test – why is it more likely to get 3 right than to get 6 right?


Try to determine the following probabilities when guessing your answers on a true or false test
Try to determine the following probabilities when guessing your answers on a true or false test:

  • 0 right

  • 1right


Try to determine the following probabilities when guessing your answers on a true or false test1
Try to determine the following probabilities when guessing your answers on a true or false test:

0 right

1right

2 right

3 right

4 right

5 right

6 right

x right


Probability Distribution for Guessing on 6 True or False Questions

http://www.mathsisfun.com/data/quincunx.html


The binomial probability distribution
The Binomial Probability Distribution Questions

  • A binomial probability is an experiment where we count the number of successful outcomes over n independent trials

    Question: Is guessing the answer on 6 true / false questions a binomial probability?


Calculating a binomial probability
Calculating a Binomial Probability Questions

  • In general, we can calculate a binomial probability of x successes on n independent trials as:

    Eg) What is the probability of guessing 4 out of 6 answers on a true or false quiz?


Try the following
Try the following: Questions

You are shooting 8 free throws and you have a 75% of scoring on each. What is the probability that you will:

  • Score on 0 shots?

  • Score on 1 shot?


Try the following1
Try the following: Questions

You are shooting 8 free throws and you have a 75% of scoring on each. What is the probability that you will:

  • Score on 0 shots?

  • Score on 1 shot?

  • Score on 2 shots?

  • Score on at least 2 shots?


You are shooting 8 free throws and you have a 75% of scoring on each. What is the probability that you will:

5. Score at least 7 shots?

6. Score 6 or 7 shots?

7. Score all of your shots except the last one?


You are shooting 8 free throws and you have a 75 chance of scoring on each
You are shooting 8 free throws and you have a 75% chance of scoring on each.

  • How many shots do you expect to score?


The expected value of a binomial
The Expected Value of a Binomial scoring on each.

  • In general, the expected value of a binomial probability is given as:

    Try: What is the expected value of

  • Guessing on 100 True / false questions?

  • Rolling a dice 600 times and counting 6s?

  • Shooting 200 baskets with a 75% chance of making each one


Try the following2
Try the following: scoring on each.

Suppose that 2% of all calculators bought from Dollarama are defective.

You randomly collect 20 of them.

What is the probability that:

  • None of them are defective?

  • 2 or more are defective?

  • In a batch of 1500, how many do you expect to be defective?


Summary
Summary: scoring on each.

What is a probability distribution?

How do you calculate a binomial probability?

What are two conditions that you need in order to use a binomial probability calculation?

Why do you multiply a binomial probability by nCx?

  • p. 385 #1, 2, 3, 5, 6bc, 7ab, 8ab, 15, 17 Challenge: 10, 11


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