Probability. Name: Slot: Essential Math 12. Introduction. Probability and Odds - Single Event. Probability and Odds - Two and Multiple Event

Transcription

1 Probability Essential Math 12 Mr. Name: Slot: Introduction Probability and Odds - Single Event Probability and Odds - Two and Multiple Event Experimental and Theoretical Probability Expected Value (Expected Win/Loss) (robability in the Workplace 1

2 2 Probability and Odds n alculate the following L s / - i- I2_-.12.;j - ) 4 3 v Introduction Probability Essential Math 12 2%of %of48 1%of42 4.z.. 12%of2O.12-55%of88 3%of4O il 5% of 8 113%of25..2!.?:c 17. t 9B Lie i -. zs 1 Th 13% l3outof 1 Percent Fraction Decimal Words Fill in the table,

3 Identify all possible outcomes:, I entify the event: white, One ball will be drawn from the bag. 3 Outcomes: Event: p Spin a spinner with four colours: red, orange, blue, and green. Outcomes: Flipping a coin Event:4 (ipi- tm Outcomes:, 3, ti,s Rolling a six-sided cube (n ) Event: 1) Given the event, identify all possible outcomes Questions - Probability and Odds f) What is The probability of drawing green or red? ) L : e) State the odds against drawing red. / r-c LLL, - : d) State the odds for drdwing green. O3 33% c) State the probability of drawing a yellow. 52&3 : 7 LcL?5 b) State all the possible outcomes; how many possible outcomes, a) State the event. Bob is drawing marbles from a bag: there are 5 green, 3 yellow and 1 red. Example 2 A bag has six balls in it. The colours are as follows: red, green, yellow, orange, black, and Example 1

4 b) alculate the probability of rolling an even number. b) State the odds for spinning red, - Q 4) The weather forecast states that there is a 3% probability of rain tomorrow. 2:2- LII c) State the odds against spinning red. e) State the odds against spinning green or blue. 2:2 d) State the odds for spinning green or blue. 3:1 3) A spinner has four colours: red, orange, blue, and green. d) alculate the probability of not rolling a 6. c) alculate the probability of rolling a number greater than 4.,teve.a) 11/ - - I J- c- SOIL Q a) alculate the probability of rolling a 2. 2) If you roll a six-sided cube (die) / 3 / 3O7o b) State the odds for it raining tomorrow, 7o 3 a) State the odds against it raining tomorrow. 1 (- - a) alculate the probability of not spinning blue

5 a) Probability of picking an even number 5) There are ten numbers in a hat numbered lthrough 1. A ball is drawn at random, Odds and ProbabiUty - Two Event & MuItpIe Event y 1 7) Identify a situation where the odds are 5:2. c) Fraction b) Percent L1(1. a) Decimal 6) The odds of snow this Tuesday is 5:4. Express the probability of it not rqirn as e) State the odds for drawing a four. 3 d) State the odds against drawing a number more than 4. s+l c) State the odds against drawn a numberless Than 3. b) State the odds for picking a 7. I, z 3, -1, I S

6 Make a probability tree and a matrix to make, 2 1 I 6 L1L1 I 2( Z. ) ç2,) ( ) I J a list of all outcomes. then second ball is drawn. There are 4 balls in a hat numbered lthrough 4. A ball is drawn and returned to the hat and 19 b s-o Make a probability tree to list all possible outcomes. OutcomesforEventi:. OutcomesforEvent2: O.J_? s? u Event 1: Event 2: 3 1. is spun at the same time. A six-side cube (die) is rolled and a spinner with the colours: orange, yellow, brown and grey Example 1 Example 2 cc 2. %%%% 3! ] -L State the event and their individual outcomes

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8 ) a) State the probability of rolling 1 and 1 (snake eyes). -. L. I.-----i 3 b) State the probability of flipping one head and one tail. 2) A coin is flipped Iwice. e) State the odds ef spinning one blue and one red (order does not maffer). d) State the probability of not spinning red, red? ( 8 b) State the odds against rolling a sum less than 5.?. ( 2 1 L 3 L. 3) Two dice are rolled. j i.f a) State the probability of flipping heads, heads.

9 L3 4) April and Ryan will have four children. JL( b) What are the odds for having 4 children of the same gender? a) What is the probabilhy that they will have at least 3 girls? 3-73I I D 9

10 1 ( b) State the experimental probability of flipping a tails. U c) Is it possible that 6 is rolled 12 consecutive times? Questions - Experimental - 1&L b) State the experiment probability, a) State the theoretical probability of rolling a 6 a) State the theoretical probability of flipping a heads. 1) A coin is flipped 974 times and it has been heads 532 times. A die is rolled 542 times and a 6 occurs 151 times. Example 1 Experimental and Theoretical Probability and Theoretical Probability / / t

11 b) State the theoretical probability. a) State the experiment probability. 11 quality control specialist be concerned that too many widgets are defective? Explain. day he notices that there were 2 of 2 widget made were defective. Should the 6) A quality control specialist at a factory knows that 2% of widgets are defective. On a / /, / H b) What is the probability flipping a heads on the next flip. Explain, a) State the experimental probability, heads. 5) You flip a coin five times and the following occurred: heads, heads, tails, heads, A every 9 óups correct? Please state your reasoning. insists that the statement 1 out of every 9 cups is a winner must be wrong. Is 1 out of approximately 1 out 9. Jessica buys 9 cups of coffee and did not get a winner, She 4) A cup from Tim Horton s Roll up the Rim to Win contest being a winner is f32) (13 3 ff3 people to you expect to have leff handed. 3) The probability of being left handed is approximately 1 in 11. Out of 13,25 how many 5, 1,3,5,2, 2) You are roll a six-sided cube (die) times, The outcomes of the six rolls are as follows:

12 12, fl 9) State an example where having an item failing.1 % unacceptable. F4c -.Lj A ) Explain why Erwin might decide to plant canola even though most farmers in the 5 b) State the experimental probability that a surveyed farmer will plant canola. a) State the theoretical probability that a surveyed farmer will plant wheat. and finds out that 7 of them plan to plant wheat. area will plant one of two crops: wheat or âeiwiñiüi7eys 1 farmers in the area area are planning to plant wheat. 7) Erwin is a farmer in rural Manitoba. The isan equal probabwty that a farmer in Erwin s 8) State an example where having an item failing 1% of the time is acceptable. (IL

13 select the correct card, you win $4.. alculate the expected win/loss. Interpret the meaningofthisnumber. pil) A card game has five cards, one of which is the winner, The game costs $1. to play. If you ikampie 1 E(V) = P(win) gain P(loss) loss ca, - LA. -S 1 ii?( expected value. Should she bid on the contract? contract. She calculates the expected value to be $425. Interpret the meaning of the achel owns a window cleaning company. She is considering puffing in a bid for a - 1 5q_ )(3) -Mc.) ( v) -( ( Expected Value (Expected Win/Loss) 13

14 14 (E) \_: -, e. Pay $1. Toss Iwo coins. If they are both heads, you win $ ) (sc I)! \ proposal. Is it financially a good idea for her to bid on the contract? $2,4 to prepare a contract proposal. Find the expected win/loss of the contract = /1?(s ItS; soo 2 7-) (2)?(/sJ(is3) winning a contract is.3. The contract is worth $25, and she knows it will cost her 1) Based on past experience, a building contractor estimates that the probability of L j Questions - Expected Value (Expected Win/Loss) c 1 13 L 1- a. Pay $1. Toss a coin, If it shows heads, you win $2. even, if played many times. Z2. c) 7 5 oo OO 4 I bs ) 1 foss I : (3 ti ( I ) L..4, I i -1 1 ri P( d. Pay$1, Rolladie. lfa2or3shows,youget$4. lc5)( (D1 (L.) cd( ) c. Pay $2. Draw a card from a shuffled deck, If it is a jack or an ace, you get $1, b. Pay $1. Draw a card from a shuffled deck, If it is a heart you get $5. ) () ft)o) 2) For each of the following games determine whether you would win, lose, or break -$ sic

15 2o S - (.1sj(1Foc) a) Find the expected value of the contract proposal. How much will the engineer gain if he wins the contract? P(-) -y.. ) Q One c. Is it financially a good idea for the company to send out flyers? Please explain :[(9 (rj b. Find the expected value of 1 flyers., 2 = P() ((s) (1s a. Find the expected value of each flyer. carpets it cleans. It costs the company $.25 for each flyer. average, the company makes a profit of $5. on each household whose that on average 1 out of every 1 households receiving its flyer will use its service, 4) A carpet cleaning company uses flyers to promote its business. The company knows E J-. Ip b) Is it financially a good idea for the engineer to bid on the contract? Explain. (O 15 it would cost $1,8 to prepare a contract proposal. computer contract at.25. The contract is worth $1, and the engineer calculates 3) Based on past experience, a systems engineer sets the probability of winning a

16 16 p(i) I, ) f(,jr) widgets this year? plans on building 1 this year. Will the manufacturer make or lose money on 6) A manufacturer builds and sells widgets. He know that, on average, 13 widgets per purchase more tickets? b) How does the expected value change if you buy five of these tickets? Is it beffer to - a) What is your expected value if you had bought only one of the tickets? are 25 tickets sold. 5) A community club raffles off a $15 big screen TV. The tickets each cost $5 and therd 1 are defective. It costs $12 to build each widget and they sell for $18 each. He

17 test all received a mark higher than 9%. Did he make the test too easy? Please provide rationale. 1) Mr. Morin has 48 students in Essential Math 12. When he is marking, five of the first six 17 4) Identify when landscaping companies and golf courses use probability in its operation. Please provide rationale, I accident is. Evaluate this statement. her record is flawless. Amy, Nancy s boss, states the probability that Nancy will get into an D) Nancy is an excellent forklift operator. She has 33 years experience without an accident: () 2) Paul is building a fence and needs 35 usable boards. At the lumber store the probability that a board will be useable is 85%. How many boards should Paul buy? Please explain. EDrobability in the Workplace

18 18 a) Identify when Manitoba Public Insurance uses probability in its business. a row, He expresses great concern to his boss. Was his concern justified? Explain. 5) At the casino, a roulette dealer noticed that the number 22 has occurred 3 times in