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

Gameshow Problem The 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 prize 2. 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?

The Monty Hall Problem https://www.youtube.com/watch?v=mhlc7peGlGg

https://www.youtube.com/watch?v=WKR6dNDvHYQ The other way

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

Probability = Happiness over Everything

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

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

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?

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 4 cm. Area of Shaded A = 82 - (4)2 Area of a Square A = (side)2 A = (8)2 P(Sh.Reg) =

6 cm. 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) =

Given: a Box of 5 BLUE pencils & 4 RED Pencils 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)? B B B B B R R R R M M M M M M W W W

Odds vs Probability If Probability = , then ODDS =

Odds are Happiness vs Sadness

OR 1:5 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

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 There are 6 possible outcomes. Only 1 outcome corresponds to rolling a 5. Number of ways to roll the die P(rolling a 5) = Number of ways to roll a 5 = 1 6

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

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

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

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

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

GUIDED PRACTICE for Examples 1 and 2 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 ANSWER 1 362,880 The probability would decrease to 1 6

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 Odds in favor of drawing a 10 Number of non-tens = Number of tens = 4 48 = 1 12 , or 1:12

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

EXAMPLE 4 Find an experimental probability 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 SOLUTION The total number of people surveyed is: 463 + 1085 + 879 + 551 + 300 + 238 = 3516 Of those surveyed, 551 + 300 + 238 = 1089 would prefer to be at least 40. 1089 3516 P(at least 40 years old) = 0.310

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

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

GUIDED PRACTICE for Examples 3 and 4 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? ANSWER a. about 0.69 b. about 0.56

EXAMPLE 5 Find a geometric probability 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? SOLUTION P(10 Points) = Area of entire board Area of smallest circle 182 π 32 = 324 9π 36 π 0.0873

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

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

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

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.