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Conditional Probability and Multiplication Rule Section 3.2 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. Gender male Associate 231 Level Bachelor’s 553 Of Master’s 197 Degree Doctorate 25 Total 1006 female 401 769 270 20 1460 Total 632 1322 467 45 2466 Find the probability of randomly selecting someone who: Earned a bachelor’s degree 1322/2466=.536 Earned a bachelor’s degree given that the person is a female 769/1460=.527 Is a female given the person earned a bachelor’s degree 769/1322=.582 Classify as independent or dependent events P(A)=.2, P(B)=.3, P(A and B)=.06 .2*.3=.06 INDEPENDENT P(A)=.5, P(B)=.2, P(A and B)=.12 .5*.2=.1 DEPENDENT 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? 4/52*4/51=0.006 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. 1/5*1/5=0.04 At least one…. At least one means not 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) 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? ½* ½* ½* ½* ½* ½=0.016 What is the probability that you will answer at least one question correctly? 1-0.016=..984 Exercises Pg 134-139 #10-17