Conditional Probability with Two-Way Tables

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What is Conditional Probability?

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

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What is a Two-Way Table?

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A table that displays the frequency distribution of two categorical variables.

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How do you calculate Conditional Probability using a Two-Way Table?

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Divide the frequency of the event of interest by the total frequency of the condition.

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What does P(A|B) represent?

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The probability of event A occurring given that event B has occurred.

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What is the formula for Conditional Probability?

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P(A|B) = P(A and B) / P(B) if P(B) > 0.

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What is the significance of the marginal totals in a Two-Way Table?

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They show the total counts for each category, helping to understand the overall distribution.

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What is the probability that a student plays an instrument given they do not play a sport?

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Use the formula P(Instrument|No Sport) = P(Instrument and No Sport) / P(No Sport).

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If 48 male and 52 female students are surveyed, how do you find the proportion of males?

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Divide the number of males by the total number of students: 48 / (48 + 52) = 0.48.

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What is the probability of choosing a Honda from a group of cars?

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Calculate by dividing the number of Hondas by the total number of cars.

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How do you interpret the results of a Two-Way Table?

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Analyze the frequencies to determine relationships between the two categorical variables.