Example 10.23 Compute the probability of obtaining a score of 11 on a single roll of two dice. MA202 Sections 5 & 401 Chapter 10-4 Slides
Example 10.23 Compute the probability of obtaining a score of 11 on a single roll of two dice. MA202 Sections 5 & 401 Chapter 10-4 Slides
Example 10.24 Compute the probability of obtaining a score of 5 or 8 on a single roll of two dice. MA202 Sections 5 & 401 Chapter 10-4 Slides
Example 10.24 Compute the probability of obtaining a score of 5 or 8 on a single roll of two dice. MA202 Sections 5 & 401 Chapter 10-4 Slides
Example 10.25 Compute the probability of drawing a face card or a diamond at random from an ordinary deck of playing cards. MA202 Sections 5 & 401 Chapter 10-4 Slides
Example 10.25 Compute the probability of drawing a face card or a diamond at random from an ordinary deck of playing cards. MA202 Sections 5 & 401 Chapter 10-4 Slides
Example 10.26 Age 3 Age 4 Boys 8 3 Girls 6 7 Choose a student at random: What is the probability that the student is 3 years old? MA202 Sections 5 & 401 Chapter 10-4 Slides
Example 10.26 Age 3 Age 4 Boys 8 3 Girls 6 7 Choose a student at random: What is the probability that the student is 3 years old? What is the probability that the student is 3 years old, given that a boy was selected? MA202 Sections 5 & 401 Chapter 10-4 Slides
Example 10.27 A red die and a white die are rolled. What is the probability of obtaining an even number on the red die and a multiple of three on the white die? MA202 Sections 5 & 401 Chapter 10-4 Slides
Example 10.27 A red die and a white die are rolled. What is the probability of obtaining an even number on the red die and a multiple of three on the white die? MA202 Sections 5 & 401 Chapter 10-4 Slides
Example 10.27 (visually) MA202 Sections 5 & 401 Chapter 10-4 Slides
Example 10.28 An urn contains three identical red and two identical black balls. Two balls are drawn one after the other without replacement. What is the probability that the first ball is red? MA202 Sections 5 & 401 Chapter 10-4 Slides
Example 10.28 An urn contains three identical red and two identical black balls. Two balls are drawn one after the other without replacement. What is the probability that the first ball is red? MA202 Sections 5 & 401 Chapter 10-4 Slides
Example 10.28 An urn contains three identical red and two identical black balls. Two balls are drawn one after the other without replacement. What is the probability that the second ball is red given that the first ball was red? MA202 Sections 5 & 401 Chapter 10-4 Slides
Example 10.28 An urn contains three identical red and two identical black balls. Two balls are drawn one after the other without replacement. What is the probability that the second ball is red given that the first ball was red? MA202 Sections 5 & 401 Chapter 10-4 Slides
Example 10.28 An urn contains three identical red and two identical black balls. Two balls are drawn one after the other without replacement. What is the probability that both balls are red? MA202 Sections 5 & 401 Chapter 10-4 Slides
Example 10.28 An urn contains three identical red and two identical black balls. Two balls are drawn one after the other without replacement. What is the probability that both balls are red? MA202 Sections 5 & 401 Chapter 10-4 Slides
Example 10.29 Boys Girls Mr. Fleck’s Class 10 13 Mrs. Patero’s Class 12 11 A picnic committee of six people is selected at random from both classes: What is the probability that all the committee members are girls? MA202 Sections 5 & 401 Chapter 10-4 Slides
Example 10.29 Boys Girls Mr. Fleck’s Class 10 13 Mrs. Patero’s Class 12 11 A picnic committee of six people is selected at random from both classes: What is the probability that all the committee members are girls? What is the probability that all the committee members are girls, given that all come from Mr. Fleck’s class? MA202 Sections 5 & 401 Chapter 10-4 Slides
Example 10.29 Boys Girls Mr. Fleck’s Class 10 13 Mrs. Patero’s Class 12 11 A picnic committee of six people is selected at random from both classes: What is the probability that all the committee members are girls? What is the probability that all the committee members are girls, given that all come from Mr. Fleck’s class? What is the probability that the committee has three girls and three boys? MA202 Sections 5 & 401 Chapter 10-4 Slides
Example 10.29 Boys Girls Mr. Fleck’s Class 10 13 Mrs. Patero’s Class 12 11 A picnic committee of six people is selected at random from both classes: What is the probability that all the committee members are girls? What is the probability that all the committee members are girls, given that all come from Mr. Fleck’s class? What is the probability that the committee has three girls and three boys? What is the probability that the committee has three girls and three boys given that Mary Akers and Ann-Marie Harborth are on the committee? MA202 Sections 5 & 401 Chapter 10-4 Slides
Example 10.30 Compute the probability of obtaining a score of at least 4 on a single roll of two dice. MA202 Sections 5 & 401 Chapter 10-4 Slides
Example 10.30 Compute the probability of obtaining a score of at least 4 on a single roll of two dice. MA202 Sections 5 & 401 Chapter 10-4 Slides
Example 10.31 A hand of 5 cards is drawn from a standard 52-card deck. What is the probability that both colors (red and black) are represented in the hand? MA202 Sections 5 & 401 Chapter 10-4 Slides
Example 10.31 A hand of 5 cards is drawn from a standard 52-card deck. What is the probability that both colors (red and black) are represented in the hand? What is the complement of this event? MA202 Sections 5 & 401 Chapter 10-4 Slides
Example 10.31 A hand of 5 cards is drawn from a standard 52-card deck. What is the probability that both colors (red and black) are represented in the hand? What is the complement of this event? What is the probability that the hand is all black or all red? MA202 Sections 5 & 401 Chapter 10-4 Slides
Properties of Probability Theorem 1 P ( A ) = 0 if and only if A cannot occur. 2 P ( A ) = 1 if and only if A always occurs. 3 For any event A, 0 ≤ P ( A ) ≤ 1 . 4 For any events A and B, P ( A ∪ B ) = P ( A ) + P ( B ) − P ( A ∩ B ) . 5 If A and B are mutually exclusive events, then P ( A ∩ B ) = 0 . 6 For any events A and B, P ( A ∩ B ) = P ( A ) P ( B | A ) . 7 If A and B are independent events, then P ( B | A ) = P ( B ) . 8 If E and E are complementary events, then P ( E ) + P ( E ) = 1 . MA202 Sections 5 & 401 Chapter 10-4 Slides
Example 10.33 In the game of craps, one wins on the first roll of the pair of dice if a 7 or 11 is thrown. What are the odds of winning on the first roll? MA202 Sections 5 & 401 Chapter 10-4 Slides
Example 10.33 In the game of craps, one wins on the first roll of the pair of dice if a 7 or 11 is thrown. What are the odds of winning on the first roll? MA202 Sections 5 & 401 Chapter 10-4 Slides
Examples 10.34 and 10.35 Ex. 10.34: If the odds in favor of event E are 5 to 4, compute P ( E ) and P ( E ). MA202 Sections 5 & 401 Chapter 10-4 Slides
Examples 10.34 and 10.35 Ex. 10.34: If the odds in favor of event E are 5 to 4, compute P ( E ) and P ( E ). Ex. 10.35: If P ( E ) = 22 / 52 compute the odds in favor of E and the odds against E . MA202 Sections 5 & 401 Chapter 10-4 Slides
Example 10.36 An American roulette wheel has 38 numbered compart- ments: green 0 and 00, and 1-36 alternating red and black. One way to bet is to bet on red or black. If the ball lands in that color, you win the amount of your bet, otherwise you lose it. If you consistently bet $5 on red, what is the expected amount you win per roll? MA202 Sections 5 & 401 Chapter 10-4 Slides
Example 10.37 Suppose you are offered the opportunity to play a game that consists of a single toss of three coins. It costs you $21 to play the game, and you win $100 if you toss three heads, $20 if you toss two heads, and nothing if you toss more than one tail. Would you play the game? MA202 Sections 5 & 401 Chapter 10-4 Slides
Class Discussion Discussion questions! MA202 Sections 5 & 401 Chapter 10-4 Slides
Homework Homework 4 (due 3/2/10): Section 10.3 # 2, 4, 5, 8, 10, 11, 13, 20, 21, 25a-c, 31ab, 32 Section 10.4 # 1, 3, 4, 5, 7, 9, 10, 35 MA202 Sections 5 & 401 Chapter 10-4 Slides
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