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AP Statistics Section 6.2C Independent Events & The Multiplication Rule

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AP Statistics Section 6.2CIndependent Events & The Multiplication Rule

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

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.

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

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

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.

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

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

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

independent

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

dependent

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

dependent

Example: Are an event A and Ac independent? Why are why not?Note:

Disjoint events are not independent.

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?

Multiplication Rule for Independent Events: If A and B are independent, then___________________

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

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

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

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

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