S.CP.A.4: Conditional Probability

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What is Conditional Probability?

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Conditional Probability is the probability of an event occurring given that another event has already occurred. It is denoted as P(A|B), which means the probability of event A occurring given that event B has occurred.

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How do you determine if two events are independent?

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Two events A and B are independent if the occurrence of one does not affect the probability of the other. Mathematically, this is expressed as P(A and B) = P(A) * P(B).

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What is the formula for Conditional Probability?

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The formula for Conditional Probability is P(A|B) = P(A and B) / P(B), where P(A|B) is the probability of A given B.

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What does it mean if two events are dependent?

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Two events are dependent if the occurrence of one event affects the probability of the other event occurring.

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What is the significance of a contingency table in probability?

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A contingency table displays the frequency distribution of variables and helps in determining the relationship between them, including independence or dependence.

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How can you calculate the probability of an event given another event?

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To calculate the probability of an event A given event B, use the formula P(A|B) = P(A and B) / P(B).

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What is the relationship between gender and music preference based on survey data?

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Survey data can show whether gender and music preference are independent or dependent by analyzing the frequencies in a contingency table.

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What is an example of independent events in probability?

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An example of independent events is flipping a coin and rolling a die. The outcome of the coin flip does not affect the outcome of the die roll.

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What is an example of dependent events in probability?

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An example of dependent events is drawing cards from a deck without replacement. The outcome of the first draw affects the probabilities of the second draw.

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How do you interpret the results of a survey regarding transportation methods?

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Interpreting survey results involves analyzing the data to determine probabilities, such as the likelihood of being late based on the method of transportation.