Ap statistics section 6 2c independent events the multiplication rule
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AP Statistics Section 6.2C Independent Events & The Multiplication Rule PowerPoint PPT Presentation


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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 ?.

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AP Statistics Section 6.2C Independent Events & The Multiplication Rule

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Ap statistics section 6 2c independent events the multiplication rule

AP Statistics Section 6.2CIndependent Events & The Multiplication Rule


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?


Ap statistics section 6 2c independent events the multiplication rule

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 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

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


Ap statistics section 6 2c independent events the multiplication rule

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

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


Ap statistics section 6 2c independent events the multiplication rule

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


Ap statistics section 6 2c independent events the multiplication rule

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

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

independent


Example determine if the two events a and b are independent1

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

dependent


Example determine if the two events a and b are independent2

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

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

Disjoint events are not independent.


Disjoint and independent do not mean the same thing

Disjoint and independent do not mean the same thing.


Ap statistics section 6 2c independent events the multiplication rule

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

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


Ap statistics section 6 2c independent events the multiplication rule

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.b. rolling five 6-sided dice and getting five twos


Ap statistics section 6 2c independent events the multiplication rule

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

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


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