Conditional Probability & Independence

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What is Conditional Probability?

Back

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 A given B.

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What does P(A|B) represent?

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

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What is the definition of Independent Events?

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Independent Events are two events A and B where the occurrence of one does not affect the occurrence of the other. Mathematically, P(A|B) = P(A).

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If A and B are independent, what is P(A ∩ B)?

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If A and B are independent, then P(A ∩ B) = P(A) * P(B).

Front

What is the probability of drawing a red card from a standard deck of cards?

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The probability of drawing a red card from a standard deck of 52 cards is P(Red) = 26/52 = 1/2.

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How do you calculate the probability of two independent events both occurring?

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To calculate the probability of two independent events A and B both occurring, use the formula P(A ∩ B) = P(A) * P(B).

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What is the probability of event A occurring if P(A) = 0.3 and P(B) = 0.5, and A and B are independent?

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P(A ∩ B) = P(A) * P(B) = 0.3 * 0.5 = 0.15.

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What is the probability that a randomly chosen customer holds a Visa card given they hold an AA card?

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This is an example of conditional probability, calculated as P(Visa|AA) = P(Visa ∩ AA) / P(AA).

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What is the relationship between P(A|B) and P(A) for independent events?

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For independent events, P(A|B) = P(A).