Theoretical Probability 11.4

Theoretical Probability Lesson Objectives Find the theoretical probability of an event Vocabulary theoretical probability _________________ Additional Examples Example 1 Andy has 20 marbles in a bag. Of these, 9 are clear and 11 are blue. Find the probability of each event. Write your answer as a fraction, a decimal, and a percent. p = number of outcomes total number of '------------" outcomes marbles P(clear) = number of total number of marbles = L___I __JI = �% Write the ratio. Substitute. Write as a decimal and write as a percent. The theoretical probability of drawing a clear marble is I orLJ%. The theoretical probability of drawing a blue marble is 1 [ - J,or0%. J, LI____JI, Ci, or Example 2 There are 13 boys and 10 girls on the track team. The name of each team member is written on an index card. A card is drawn at random to choose a student to run a sprint and the card is replaced in the stack. A. Find the theoretical probability of drawing a boy's name. P(boy) = number of • ••. number of[.._ _ : on the team .. ·- . • on the team Find the theoretical probability Substitute. Try This 1. Find the probability. Write your answer as a fraction, as a decimal, and as a percent. Jane h as 20 marbles in a bag. Of these 8 are green. Find the probability of drawing a green marble from the bag. 2. There are 15 boys and 12 girls in the class. Find the theoretical probability of drawing a boy's name. The theoretical probability of an event is found by comparing the number of ways an event can occur to the total number of equally likely outcomes. . . . _ number of ways the event c n occur theoretical probability - total number of equally likely aoutcomes One of the games at a carnival is the Wheel of Letters. Find the probability that the wheel will stop on each letter. Write your answer as a fraction, as a decimal, and as a percent. 1. The spinner has ___ equal sections. Each section is an equally likely outcome. 2. There is __ section marked A. 3. There are sections marked B. 4. There are __ sections marked C. 5. There are sections marked D. % 6. P(B) = __ = 0.3 = 7.P(A)=-=0.1= 8. P(C) = _ = _ = 0.4 = % 9. P(D) =-=-= 0.2 = There are 11 pennies and 9 dimes in a bag. Find the probability of each event. Write your answer as a fraction, as a decimal, and as a percent. 1 O. Find the probability that a dime will be drawn from the bag. P(dime) = - = 0.45 = --��% 11. P(penny) = ___ = 0.55 = ___ There are 6 yellow cards, 4 blue cards, and 10 green cards In a bag. A card is chosen at random. Find the probability of each event. 12. yellow _ __ 13.blue ___ 14. green ___ 15. blue or green ___ % % Tina has 3 quarters , 1 dime, and 6 nickels in her pocket. Find the probability of randomly drawing each of the following coins. Write your answer as a fraction, as a decimal, and as a percent. Fraction Decimal Percent 1. quarter 2. dime 3. nickel Find the probability of each event. Write your answer as a fraction, as a decimal, and as a percent. Round to the nearest tenth of a percent. 4. randomly choosing a red card in a game that has 1 O red, 1 O blue, 1 o green, 1 O yellow cards, and 1 O orange cards 5. tossing two fair coins and having both land tails up 6. randomly drawing 1 of the 4 S's from a bag of 100 Scrabble tiles 7. rolling a number greater than 4 on a fair number cube A game has 12 blue disks, 10 red disks, and 8 black disks. Find the probability of each event when a disk is chosen at random. 8. red _____ 10. blue _____ 9. black _____ 11. not red or blue _____ Find the probability of each event. Write your answer as a fraction, as a decimal, and as a percent. Round to the nearest tenth of a percent. 1. randomly choosing a white counter from a bag of 12 red counters, 12 white counters, 12 green counters, and 12 blue counters 2. tossing two fair coins and having one land on tails and one land on heads 3. rolling a number greater than 1 on a fair number cube 4. randomly drawing an orange disk from a bag of 14 black disks, 4 blue disks and 12 orange disks 5. randomly drawing 1 of the 6 R's from a bag of 100 Scrabble tiles 6. spinning a number less than 7 on a fair spinner with 8 equal sections labeled 1-8 A set of cards has 20 cards with stars, 10 cards with squares, and 15 cards with circles. Find the probability of each event when a card is chosen at random. 7. square _____ 9. star or circle _____ 8. circle _____ 10. not circle or square _____ There are 14 girls and 18 boys in Ms. Wiley's class. Ms. Wiley randomly selects one student to solve a problem. Find the probability of each event. 11. selecting a boy _____ 12. selecting a girl _____ Find the probability of each event. Write your answer as a fraction, as a decimal, and as a percent. Round to the nearest tenth of a percent. 1. tossing three fair quarters and having all three of them land on heads 2. randomly choosing a classical CD from a collection of CDs consisting of 35 jazz CDs, 20 classical CDs, 25 rock CDs, and 5 country music CDs 3. randomly choosing a card with an even number from a shuffled deck of 52 cards with four 13-card suits (diamonds, hearts, clubs and spades), each of which has 9 number cards labeled 2-1O and 4 other cards 4. randomly drawing a vowel from a bag of 100 Scrabble® tiles that has 12 E's, 9 I's, 8 O's, 4 U's and 2 Y's. There are 15 girls and 9 boys in Anne's yoga class. One of them is randomly selected to demonstrate a yoga position. Find the probability of each event. 5. selecting a boy _____ 6. selecting a girl _____ Find the probability of each event when two 1-6 number cubes are rolled. 7. P(total of 5) ____ 9. P(total ?.7) ____ 8. P(total of 10) ____ 10. P(total < 2) ____