Ch Probability Outcomes & Trials

Transcription

1 Learning Intentions: Ch Probability Outcomes & Trials Define the basic terms & concepts of probability. Find experimental probabilities. Calculate theoretical probabilities.

2 Vocabulary: Trial: real-world activity. ex.) # of times you flip a coin or roll a die Outcome: a possible result of one trial of an experiment. ex.) getting a heads/tails or a particular number on a die Event: any set of desired outcomes. ex.) landing on tails side of coin Probability P(x): a number between 0 and 1 that gives the chance that an outcome, x, will happen. event totals (x) landing on tails side P(x) = P(tails) = outcome totals (n) total sides of the coin 2 Theoretical probability: a probability calculated by analyzing a situation, rather than performing an experiment. ex.) P(rolling a 2) P(tails) = ½ 6 Experimental probability: probabilities based on experience/observations or collected data. a.k.a. Relative Frequency

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4 Solutions: a.) P(sock color) = # of times color was worn total # of trials P(black) = 6 15 P(white) = 7 15 P(red) = 2 15 = 0.4 = 40% = 0.46 = 46.6% = % b.) EXPERIMENTAL probability was based on actual observation.

5 Ex.) Probability: Using the candy data given below, what is the probability of selecting a green piece of candy from your bag without looking? Is this a theoretical or experimental probability? Colored Candies Manufactured Orange Yellow Blue Red Green Brown

6 Ex.) Solutions: Using your candy data, what is the probability of selecting a green piece of candy from your bag without looking? Is this a theoretical or experimental probability? Colored Candies Manufactured Orange Yellow Blue Red Green Brown Theoretical probability b/c this probability is based on analyzing the given situation, and NOT based on an actual trial or what you re about to do.

7 As part of your job with the forest service, you tagged a total of 1470 squirrels last year. You tagged 820 black male squirrels, 100 black female squirrels, 380 gray male squirrels, & 170 gray female squirrels. If this distribution accurately reflects the squirrel population, what is the probability that the next squirrel you tag will be: A.) A gray male squirrel? B.) A female squirrel? C.) A red squirrel?

8 Solutions: You tagged a total of 1470 squirrels last year. You tagged 820 black male squirrels, 100 black female squirrels, 380 gray male squirrels, & 170 gray female squirrels. What is the probability that the next squirrel you tag will be: A.) A gray male squirrel? P(gray male) = # of gray males total squirrels = 380 1,470 B.) A female squirrel? P(female) = total # of females (black+gray) total squirrels C.) A red squirrel? P(red) = # of red squirrels total squirrels = % = 270 1, % **check that individual event sum = total** 0 1,470 = 0 = 0%

9 For each trial, Trials & Outcomes list the possible outcomes. calculate the probabilities for all outcomes. create a circle graph for 2-dice-sum trial. TRIAL Outcomes Probabilities Ex.) Tossing a coin {heads, tails} P(heads) 2 P(tails) 2 = 0.5 = 50% = 0.5 = 50% Rolling a die with face #(1 6) A spinner divided into sections A E The sum when rolling 2 six-sided dice

10 Solutions: Trials and Outcomes Rolling a die with faces numbered 1 6. S: {1, 2, 3, 4, 5, 6} P(rolling 1) = P(rolling 2) = P(rolling 3) = P(rolling 4) = P(rolling 5) = P(rolling 6) = rolling 1 rolling any number 6 rolling 2 rolling any number 6 rolling 3 rolling any number 6 rolling 4 rolling any number 6 rolling 5 rolling any number 6 rolling 6 rolling any number 6 = % = % = % = % = % = % Spinning the pointer on a dial divided into sections A E. S: {A, B, C, D, E} P(A) = P(B) = P(C) = P(D) = P(E) = landing on A landing on any section 5 landing on B landing on any section 5 landing on C landing on any section 5 landing on D landing on any section 5 landing on E landing on any section 5 = 0.2 = 20% = 0.2 = 20% = 0.2 = 20% = 0.2 = 20% = 0.2 = 20% Spinner A B C D

11 Solutions:The sum when rolling 2 six-sided dice. Sums: {2 12} 11 total sums, but 36 total outcomes P(rolling sum 2) = = 2.7% P(rolling sum 12) = = 2.7% P(rolling sum 3) = 2 = 0.05 = 5.5% P(rolling 36 P(rolling sum 4) = 3 = = 8.3% P(rolling 36 P(rolling sum 5) = 4 = % P(rolling 36 sum 11) = 2 = 0.05 = 5.5% 36 sum 10) = 3 = = 8.3% 36 sum 9) = 4 = % 36 P(rolling sum 6) = 5 = % P(rolling 36 2 nd Die P(rolling sum 7) = 6 = % 36 1 st Die n = 36 total outcomes sum 8) = 5 = %

12 Test Your Knowledge For which of the following games at the school carnival could you use theoretical probability to predict the likelihood you will win the game? A.) The basketball toss where you have to get 3 baskets out of 4 attempts to win a prize B.) The target shoot where you have to shoot a moving target with a water gun 1 time out of 3 different tries C.) The dice game where you have to roll 2 six-sided number cubes that add up to 9 to win the game D.) The water balloon toss where you and your partner have to stand 10 feet apart and throw a balloon back and forth 10 times without dropping it to win a prize

13 For which of the following games at the school carnival could you use theoretical probability to predict the likelihood you will win the game? A.) The basketball toss where you have to get 3 baskets out of 4 attempts to win a prize B.) The target shoot where you have to shoot a moving target with a water gun 1 time out of 3 tries C.) Solutions: Test Your Knowledge The dice game where you have to roll 2 six-sided number cubes that add up to 9 to win the game D.) The water balloon toss where you and your partner have to stand 10 feet apart and throw a balloon back and forth 10 times without dropping it to win a prize P(sum of 9) = 4/ % ~ all other options need experimental data (your known ability at each game) to make any future predictions.