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A card is drawn from a standard deck of 52 cards. Find each probability.

WARMUP. 1. 1. ANSWER. ANSWER. 2. 4. 1. ANSWER. 13. Lesson 10.4 , For use with pages 707-713. A card is drawn from a standard deck of 52 cards. Find each probability. 1. P (a red card). 2. P (a ten). 3. What is the probability that two flipped coins show heads?.

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A card is drawn from a standard deck of 52 cards. Find each probability.

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  1. WARMUP 1 1 ANSWER ANSWER 2 4 1 ANSWER 13 Lesson 10.4, For use with pages 707-713 A card is drawn from a standard deck of 52 cards. Find each probability. 1. P(a red card) 2. P(a ten) 3. What is the probability that two flipped coins show heads?

  2. 10.4 Notes - Finding Probability of Disjoint and Overlapping Events BlackJack Tutorial #1 (3min) http://www.youtube.com/watch?v=W4QPE0GeUfw&feature=related Craps Tutorial #2 (4min) http://www.youtube.com/watch?v=vKWBZXX8hYU&feature=relmfu

  3. Objective -To find probabilities of union and intersections of two events. To use the complement to find the probability of an event.

  4. B A Union of A and B

  5. B A Intersection of A and B

  6. Intersection of A and B is the empty set. A B A and B are Mutually Exclusive

  7. Probability of Mutually Exclusive Events A die is rolled one time. What is the probability of rolling a 2 or 6? A card is randomly selected from a standard deck of 52 cards. What is the probability that it is a 2 or a king?

  8. Probability of a Compound Event A die is rolled one time. What is the probability of rolling an odd number or a prime number? Prime #’s: 2,3,5 Odd #’s: 1,3,5 A card is randomly selected from a standard deck of 52 cards. What is the probability that it is a red card or a king?

  9. Using Intersection to Find Probability Twenty-five students are on the Jefferson Middle School football team. Six of them take Algebra, 12 of them took Biology and 15 students took Algebra or Biology. What is the probability that a student took both Algebra and Biology?

  10. Probability of the Complement of an Event The event A´ (A prime), is called the complement of event A, consists of all the outcomes that are not in A. A card is randomly selected from a standard deck of 52 cards. What is the probability that it is not a spade?

  11. Events A and B are mutually exclusive. Find P(A or B).

  12. MONEYBALL VIDEO 1 (2min)Money Ball Video 2 (2min)

  13. Let event Abe selecting a 10 and event Bbe selecting a face card. Ahas 4 outcomes and Bhas 12 outcomes. Because Aand Bare disjoint, the probability is: 4 4 16 12 0.308 = = + = 13 52 52 52 EXAMPLE 1 Find probability of disjoint events A card is randomly selected from a standard deck of 52 cards. What is the probability that it is a 10or a face card? SOLUTION P(A orB) = P(A)+ P(B)

  14. SOLUTION Let event Abe selecting a face card and event Bbe selecting a spade. Ahas 12 outcomes and Bhas 13 outcomes. Of these, 3 outcomes are common to Aand B. So, the probability of selecting a face card or a spade is: EXAMPLE 2 Standardized Test Practice

  15. = P(A)+ P(B)– P(AandB) P(A orB) 12 13 3 – = + 52 52 52 22 = 52 11 = 26 ANSWER The correct answer is B. EXAMPLE 2 Standardized Test Practice

  16. Senior Class Out of 200 students in a senior class, 113 students are either varsity athletes or on the honor roll. There are 74 seniors who are varsity athletes and 51 seniors who are on the honor roll. What is the probability that a randomly selected senior is both a varsity athlete and on the honor roll? EXAMPLE 3 Use a formula to find P(A and B) SOLUTION Let event Abe selecting a senior who is a varsity athlete and event Bbe selecting a senior on the honor roll. From the given information you know that:

  17. 113 51 74 P(A) ,P(B) , andP(A orB) = = = 200 200 200 P(A orB) = P(A)+P(B)–P(A andB) 74 51 113 –P(A andB) + = 200 200 200 74 51 113 P(A andB) – + = 200 200 200 12 3 P(A andB) = = = 0.06 200 50 EXAMPLE 3 Use a formula to find P(A and B) FindP( A and B ) Write general formula. Substitute known probabilities. Solve for P(Aand B). Simplify.

  18. Selecting an ace or an eight 2 13 ANSWER for Examples 1, 2, and 3 GUIDED PRACTICE A card is randomly selected from a standard deck of 52 cards. Find the probability of the given event.

  19. A card is randomly selected from a standard deck of 52 cards. Find the probability of the given event. Selecting a 10or a diamond 0.308 ANSWER for Examples 1, 2, and 3 GUIDED PRACTICE

  20. ANSWER 0.095 P(A andB) = What If? In Example 3, suppose 32 seniors are in the band and 64 seniors are in the band or on the honor roll. What is the probability that a randomly selected senior is both in the band and on the honor roll? for Examples 1, 2, and 3 GUIDED PRACTICE

  21. Dice When two six-sided dice are rolled, there are 36 possible outcomes, as shown. Find the probability of the given event. The sum is not 6. The sum is less than or equal to 9. EXAMPLE 4 Find probabilities of complements

  22. P(sum is not 6) = 1 – P(sum is 6) 5 = 1 – 36 31 0.861 = 36 P(sum< 9) = 1 – P(sum > 9) 6 36 = 1– 30 = 36 5 0.833 = 6 EXAMPLE 4 Find probabilities of complements

  23. Fortune Cookies A restaurant gives a free fortune cookie to every guest. The restaurant claims there are 500 different messages hidden inside the fortune cookies. What is the probability that a group of 5 people receive at least 2 fortune cookies with the same message inside? The number of ways to give messages to the 5 people is 5005. The number of ways to give different messages to the 5 people is 500499498 497496. So, the probability that at least 2 of the 5 people have the same message is: EXAMPLE 5 Use a complement in real life SOLUTION

  24. P(at least2are the same) = 1 – P(none are the same) 500499498 497496 = 1 – 5005 0.0199 EXAMPLE 5 Use a complement in real life

  25. Find P( A ). P(A) = 0.45 0.55 ANSWER = for Examples 4 and 5 GUIDED PRACTICE

  26. Find P( A ). 1 3 P(A) = 4 4 ANSWER = for Examples 4 and 5 GUIDED PRACTICE

  27. Find P( A ). P(A) = 1 0 ANSWER for Examples 4 and 5 GUIDED PRACTICE

  28. Find P( A ). P(A) = 0.03 0.97 ANSWER for Examples 4 and 5 GUIDED PRACTICE

  29. ANSWER The probability increases to about 0.097. What If? In Example 5, how does the answer change if there are only 100 different messages hidden inside the fortune cookies? for Examples 4 and 5 GUIDED PRACTICE

  30. 10.4 Assignment 10.4: 3-27ALL, 44(D), 55(y = (x+7)/3) Notes for This Book 1. Complement of P: P(A’) is written as P(A) 2. Instead of the words Mutually Exclusive, this book uses the word Disjoint

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