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AP Statistics Section 6.2C Independent Events & The Multiplication Rule

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Consider a standard deck of 52 playing cards. If one card is chosen at random, what is the probability the card is red?

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If the first card is red and a second card is chosen at random from the same deck, the probability that this card is also red will depend upon what was done with the first card.

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If the first card was returned to the deck, the probability the second card is red will be…

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If the first card was not returned to the deck, the probability the second card is red will be…

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In the first case, knowing that the first card pulled from the deck was red did not affect the probability that the second card was red.

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This is not true, however, in the second case.

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In the second case, knowing that the first card pulled from the deck was red affected the probability that the second card was red.

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Two events are independent if knowing that the one occurs does not affect the probability that the other one occurs.

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Example: Determine if the two events A and B are independent. independent

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Example: Determine if the two events A and B are independent. dependent

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Example: Determine if the two events A and B are independent. dependent

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Example: Are an event A and A c independent? Why are why not? Note: Disjoint events are not independent.

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Disjoint and independent do not mean the same thing.

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Consider rolling a 6-sided die and then flipping a coin. What is the probability of rolling a 3 and getting a heads on the coin?

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Example: Find the following probabilities. a. selecting 4 cards with replacement from a standard deck and having all 4 be clubs

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Example: Find the following probabilities. b. rolling five 6-sided dice and getting five twos

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Example: Find the following probabilities. c. selecting 4 cards with replacement from a standard deck and getting at least one club

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Example: Find the following probabilities. d. rolling five 6-sided dice and getting at least one two

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