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Conditional Probability and Multiplication Rule Section 3.2
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Example 1 The table shows the estimated number of earned degrees conferred in the US in 2004 by level and gender. All numbers are in thousands. The table shows the estimated number of earned degrees conferred in the US in 2004 by level and gender. All numbers are in thousands. Gender malefemaleTotal Associate231401632 LevelBachelor’s5537691322 OfMaster’s197270467 DegreeDoctorate252045 Total100614602466
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Find the probability of randomly selecting someone who: Earned a bachelor’s degree Earned a bachelor’s degree 1322/2466=.536 1322/2466=.536 Earned a bachelor’s degree given that the person is a female Earned a bachelor’s degree given that the person is a female 769/1460=.527 769/1460=.527 Is a female given the person earned a bachelor’s degree Is a female given the person earned a bachelor’s degree 769/1322=.582 769/1322=.582
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Classify as independent or dependent events P(A)=.2, P(B)=.3, P(A and B)=.06 P(A)=.2, P(B)=.3, P(A and B)=.06.2*.3=.06 INDEPENDENT.2*.3=.06 INDEPENDENT P(A)=.5, P(B)=.2, P(A and B)=.12 P(A)=.5, P(B)=.2, P(A and B)=.12.5*.2=.1 DEPENDENT.5*.2=.1 DEPENDENT
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Example 3 You are dealt two cards successively without replacement from a standard deck of 52 playing cards. What is the probability that the first card is an ace and the second card is a jack? You are dealt two cards successively without replacement from a standard deck of 52 playing cards. What is the probability that the first card is an ace and the second card is a jack? 4/52*4/51=0.006 4/52*4/51=0.006
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Example 4 Find the probability of answering two multiple choice questions correctly if random guesses are made. Each question has five choices. Only one of the choices is correct. Find the probability of answering two multiple choice questions correctly if random guesses are made. Each question has five choices. Only one of the choices is correct. 1/5*1/5=0.04 1/5*1/5=0.04
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At least one…. At least one means not none. At least one means not none. This means to find the probability of at least one, you need to find the complement of none. This means to find the probability of at least one, you need to find the complement of none. P(at least one)=1-P(none) P(at least one)=1-P(none)
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Example 5 A true-false test has six questions. If you randomly guess the answer to each question, what is the probability you will answer no questions correctly? A true-false test has six questions. If you randomly guess the answer to each question, what is the probability you will answer no questions correctly? ½* ½* ½* ½* ½* ½=0.016 ½* ½* ½* ½* ½* ½=0.016 What is the probability that you will answer at least one question correctly? What is the probability that you will answer at least one question correctly? 1-0.016=..984 1-0.016=..984
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Exercises Pg 134-139 #10-17 Pg 134-139 #10-17
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