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AP Statistics Section 6.2C Independent 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.
This is not true, however, in the second case.
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 independent if 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 A c independent? Why are why not? Note: Disjoint events are not independent.
Disjoint and independent do not mean the same thing.
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?
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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