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Lesson 10.3 , For use with pages 698-704

WARMUP. 25. 1. 58. Lesson 10.3 , For use with pages 698-704. Write the number as a percent. 3%. ANSWER. 1. 0.03. 2. 140%. ANSWER. 62.5%. ANSWER. 3. 4. 0.0045. 0.45%. ANSWER.

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Lesson 10.3 , For use with pages 698-704

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  1. WARMUP 25 1 58 Lesson 10.3, For use with pages 698-704 Write the number as a percent. 3% ANSWER 1. 0.03 2. 140% ANSWER 62.5% ANSWER 3. 4. 0.0045 0.45% ANSWER Two-thirds of the senior class work more than 20 hours per week. Write that fraction to the nearest tenth of a percent. 5. 66.7% ANSWER 6. RailRoad cRossing look out for caRs. How do you spell that without any R’s?

  2. Gameshow ProblemThe scenario is such: you are given the opportunity to select one closed door of three, behind one of which there is a prize. The other two doors hide “goats” (or some other such “non-prize”), or nothing at all. Once you have made your selection, The Host will open one of the remaining doors, revealing that it does not contain the prize2. He then asks you if you would like to switch your selection to the other unopened door, or stay with your original choice. Do you switch? Does it matter?

  3. The Monty Hall Problemhttps://www.youtube.com/watch?v=mhlc7peGlGg

  4. https://www.youtube.com/watch?v=WKR6dNDvHYQThe other way

  5. 10.3 Notes - Define and Use Probability Craps Tutorial http://www.youtube.com/watch?v=WWweWwxQnws&feature=related Roulette Simulator http://roulette-simulator.info/live-simulator/?lang=en

  6. Probability = Happiness over Everything

  7. 2 1 3 8 4 7 6 5 Objective -To find theoretical, experimental and geometric probabilities. P(factors of 8)= P(3)= P(9)= P(prime #)=

  8. Probability • Probability of Success: • Probability of Failure: s = # of ways to Succeed f = # of ways to Fail Probabilities MUST be between 1 & 0

  9. Four cards are drawn from a standard 52-card deck. What is the probability that the first three cards are black? Five cards are drawn from a standard 52-card deck. What is the probability that the first five cards are spades?

  10. 4 cm. Find the probability of throwing a dart and hitting the shaded region if you hit the square. Area of a Circle A = r2 A = (4)2 Area of Shaded A = 82 - (4)2 Area of a Square A = (side)2 A = (8)2 P(Sh.Reg) =

  11. Find the probability of throwing a dart and hitting the shaded region if you hit the rectangle. Remember your 30-60-90 Triangles: Area of  = ½  base  ht Area of  = base  ht 3 6 cm. P(Sh.Reg) =

  12. B B B B BR R R R • Given: a Box of 5 BLUE pencils & 4 RED Pencils. If a Pencil is chosen at random, what is the P(Blue)? 2. 6 Men and 3 Women: If 2 people are chosen at random, What is P(Both Women)? M M M M M M W W W

  13. Odds vs Probability If Probability = , then ODDS =

  14. Odds are Happiness vs Sadness vs

  15. 1. What are the ODDS of rolling a 3 on a six sided die? 2. 52 Card Deck: Draw 5 Cards. What are the ODDS the 1st 4 cards drawn will be HEARTS and the 5th card a SPADE? OR 1:5

  16. There are6possible outcomes. Only 1outcome corresponds to rolling a 5. Number of ways to roll a 5 P(rolling a5) = Number of ways to roll the die 1 = 6 EXAMPLE 1 Find probabilities of events You roll a standard six-sided die. Find the probability of (a) rolling a 5 and (b) rolling an even number. SOLUTION

  17. A total of 3outcomes correspond to rolling an even number: a 2, 4, or 6. Number of ways to roll an even number = Number of ways to roll the die 3 1 = 6 2 = EXAMPLE 1 Find probabilities of events P(rolling even number)

  18. What is the probability that the musicians perform in alphabetical order by their last names? (Assume that no two musicians have the same last name.) EXAMPLE 2 Use permutations or combinations Entertainment A community center hosts a talent contest for local musicians. On a given evening, 7 musicians are scheduled to perform. The order in which the musicians perform is randomly selected during the show.

  19. There are 7! different permutations of the 7musicians. Of these, only 1is in alphabetical order by last name. So, the probability is: 1 P(alphabetical order) 1 = 7! = 5040 EXAMPLE 2 Use permutations or combinations SOLUTION ≈ 0.000198

  20. There are 7C2different combinations of 2 musicians. Of these, 4C2are 2 of your friends. So, the probability is: 4C2 P(first2performers are your friends) = 7C2 6 2 = = 21 7 0.286 EXAMPLE 2 Use permutations or combinations

  21. A perfect square is chosen. 1 ANSWER = 5 for Examples 1 and 2 GUIDED PRACTICE You have an equally likely chance of choosing any integer from 1 through 20. Find the probability of the given event.

  22. A factor of 30 is chosen. 7 ANSWER = 20 for Examples 1 and 2 GUIDED PRACTICE You have an equally likely chance of choosing any integer from 1 through 20. Find the probability of the given event.

  23. What If?In Example 2, how do your answers to parts (a) and (b) change if there are 9 musicians scheduled to perform? The probability would decrease to 1 1 6 The probability would decrease to ANSWER 362,880 for Examples 1 and 2 GUIDED PRACTICE

  24. Odds in favor of drawing a 10 Number of tens = Number of non-tens 4 = 48 1 , or 1:12 = 12 EXAMPLE 3 Find odds A card is drawn from a standard deck of 52 cards. Find (a) the odds in favor of drawing a 10 and (b) the odds against drawing a club. SOLUTION

  25. Odds against drawing a club Number of non-clubs = Number of clubs 39 = 13 3 , or 3:1 = 1 EXAMPLE 3 Find odds

  26. Survey The bar graph shows how old adults in a survey would choose to be if they could choose any age. Find the experimental probability that a randomly selected adult would prefer to be at least 40 years old. EXAMPLE 4 Find an experimental probability

  27. 463 + 1085 + 879 + 551 + 300 + 238 = 3516 1089 0.310 P(at least40years old) = 3516 EXAMPLE 4 Find an experimental probability SOLUTION The total number of people surveyed is: Of those surveyed,551 + 300 + 238 = 1089would prefer to be at least40.

  28. In favor of drawing a heart ANSWER 1 3 for Examples 3 and 4 GUIDED PRACTICE A card is randomly drawn from a standard deck. Find the indicated odds.

  29. Against drawing a queen ANSWER 12 1 for Examples 3 and 4 GUIDED PRACTICE A card is randomly drawn from a standard deck. Find the indicated odds.

  30. What If?In Example 4, what is the experimental probability that an adult would prefer to be (a) at most 39 years old and (b) at least 30 years old? a.about 0.69 ANSWER b.about 0.56 for Examples 3 and 4 GUIDED PRACTICE

  31. Darts You throw a dart at the square board shown. Your dart is equally likely to hit any point inside the board. Are you more likely to get 10 points or 0 points? Area of smallest circle P(10 Points) = Area of entire board π 32 9π π 0.0873 = = = 182 324 36 EXAMPLE 5 Find a geometric probability SOLUTION

  32. Area outside largest circle P(0 points) = Area of entire board 182 – (π 92) = 182 324 – 81π = 324 4 – π = 4 0.215 Because 0.215 > 0.0873, you are more likely to get 0 points. ANSWER EXAMPLE 5 Find a geometric probability

  33. What If?In Example 5, are you more likely to get 5 points or 0 points? Because 0.2616 > 0.215, you are more likely to get 5 points. ANSWER for Example 5 GUIDED PRACTICE

  34. Area outside largest circle P(0 points) = Area of entire board 182 – (π 92) = 182 324 – 81π = 324 4 – π = 4 0.215 Because 0.2616 > 0.215, you are more likely to get 5 points. ANSWER EXAMPLE 5 Find a geometric probability

  35. 10.3 Assignment 10.3: 3-39 ODD, 50(3), 51(1), 52(2), 53(9), 58(56), 60(35) Numbers in parenthesis are the answers to those problems. You still need to show work. 50-53 are log problems. Look in the solution manual or Chapter 7 in the book for help. Experimental probability is data given in a chart from an experiment that ACTUALLY happened. Theoretical probability is what we’ve been doing where we calculate what SHOULD happen.

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