
Contents
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What is an eyeball event?
What is an eyeball event?
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Why is it called a Venn diagram?
Why is it called a Venn diagram?
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What is the probability that a person in universe U is in group A?
What is the probability that a person in universe U is in group A?
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What about people who are not in group A?
What about people who are not in group A?
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I’m sick of eyeballs. Can we consider another characteristic?
I’m sick of eyeballs. Can we consider another characteristic?
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Can we look at both characteristics simultaneously?
Can we look at both characteristics simultaneously?
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Is it possible to have Morton’s toe AND be a lefty?
Is it possible to have Morton’s toe AND be a lefty?
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Is it possible NOT to have Morton’s toe if you are a lefty?
Is it possible NOT to have Morton’s toe if you are a lefty?
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What if five lefties also have Morton’s toe?
What if five lefties also have Morton’s toe?
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We’ll run with this example for the rest of the chapter. We’ll run with this example for the rest of the chapter.
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Of the four events (A, ∼A, B, and ∼B), which are not mutually exclusive?
Of the four events (A, ∼A, B, and ∼B), which are not mutually exclusive?
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Are any events mutually exclusive?
Are any events mutually exclusive?
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If you were one of the lucky 100 people included in the universe, where would you fall in this diagram?
If you were one of the lucky 100 people included in the universe, where would you fall in this diagram?
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What does this have to do with probability?
What does this have to do with probability?
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What is the probability that a person selected at random is a righty and has Morton’s toe?
What is the probability that a person selected at random is a righty and has Morton’s toe?
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What does the word “marginal” mean?
What does the word “marginal” mean?
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Can you fill in the empty cells in Table 2.7?
Can you fill in the empty cells in Table 2.7?
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Quickly: What is the marginal probability of having Morton’s toe with this conjoint table?
Quickly: What is the marginal probability of having Morton’s toe with this conjoint table?
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Can you express the marginal probability of having Morton’s toe as the sum of joint probabilities?
Can you express the marginal probability of having Morton’s toe as the sum of joint probabilities?
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Can we look at this problem from the Venn diagram perspective again?
Can we look at this problem from the Venn diagram perspective again?
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If you have Morton’s toe, does that influence your probability of being a lefty?
If you have Morton’s toe, does that influence your probability of being a lefty?
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What is conditional probability?
What is conditional probability?
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How exactly do you calculate the probability that a person is a lefty, given the person has Morton’s toe?
How exactly do you calculate the probability that a person is a lefty, given the person has Morton’s toe?
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So if you have Morton’s toe, does that influence your probability of being a lefty?
So if you have Morton’s toe, does that influence your probability of being a lefty?
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Does Pr(A | B) = Pr(B | A)?
Does Pr(A | B) = Pr(B | A)?
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Can you calculate the conditional probability of being a lefty, given you have Morton’s toe, from our conjoint table instead of the raw numbers?
Can you calculate the conditional probability of being a lefty, given you have Morton’s toe, from our conjoint table instead of the raw numbers?
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Can you calculate conditional probability of having Morton’s toe, given you are a lefty, from our conjoint table?
Can you calculate conditional probability of having Morton’s toe, given you are a lefty, from our conjoint table?
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If we know the conditional and marginal probabilities, can we calculate the joint probabilities?
If we know the conditional and marginal probabilities, can we calculate the joint probabilities?
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Are Pr(A | B) and Pr(B | A) related in some way?
Are Pr(A | B) and Pr(B | A) related in some way?
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2 Joint, Marginal, and Conditional Probability
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Published:May 2019
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Abstract
This chapter introduces additional terms and concepts used in the study of probability, including Venn diagrams, independent events, and dependent events. The chapter focuses on two characteristics observed at the same time. In the example given in the chapter, the characteristics are eye dominance (i.e., left eye dominance or right eye dominance) and the presence or absence of “Morton’s toe” (Morton’s toe is a large second metatarsal which is longer than that the first metatarsal, or big toe; less than 20% of the human population has this condition). The chapter then analyses the distribution of these characteristics, both separately and simultaneously. In doing so, the chapter introduce the important concepts of joint probability, marginal probability, and conditional probability.
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