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M119L11to12

# M119L11to12 - (Lesson 11 Multiplication Rule 4-4 4.14...

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(Lesson 11: Multiplication Rule; 4-4) 4.14 LESSON 11: MULTIPLICATION RULE (SECTION 4-4) PART A: INDEPENDENT EVENTS Example 1 Pick (or “draw”) a card from a standard deck of 52 cards with no Jokers. (Know this setup!) P 3 ( ) = 4 52 = 1 13 (The 13 ranks are equally likely.) P hearts ( ) = 13 52 = 1 4 (The 4 suits are equally likely.) P 3 and hearts ( ) = 1 52 (The 52 cards are equally likely.)

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(Lesson 11: Multiplication Rule; 4-4) 4.15 The events “3” and “Hearts” are independent events, because knowing the rank of a card tells us nothing about its suit, and vice-versa. The occurrence of one event does not change our probability assessment for the other event. The rank and the suit of an unknown card are independent random variables, which we will discuss later. Dependent events are events that are not independent. Multiplication Rule for Independent Events If events A , B , C , etc. are independent, then: P A and B ( ) = P A ( ) P B ( ) P A and B and C ( ) = P A ( ) P B ( ) P C ( ) , etc. Tree Diagram Example 2 Draw three cards from a standard deck with replacement. (“With replacement” means that, after we draw a card, we place it back in the deck before we draw the next card.) Find the probability that we draw an Ace first, a King second, and a King third. Think: AKK sequence.
(Lesson 11: Multiplication Rule; 4-4) 4.16 Solution to Example 2 Because we are drawing cards with replacement, the draws are independent.

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