Experimental & Theoretical Probability

Transcription

1 Experimental and.notebook Click on an object. hat is the outcome? Experimental & Theoretical Click to go to Table of Contents of an event Experimental number of times the outcome happened number of times experiment was repeated Flip the coin 5 times and determine the experimental probability of heads. Heads Tails Experimental Example 1 olf A golf course offers a free game to golfers who make a hole in one on the last hole. Last week, out of 1 golfers achieved this. Find the experimental probability that a golfer makes a hole in one on the last hole. P(hole in one) # of successes # of trials Out of 31 golfers, you could expect 6 to make a hole in one on the last hole. Or there is a 19% chance of a golfer making a hole in one on the last hole. Experimental Example Surveys Of the first visitors through the turnstiles at an amusement park, 8 visitors agreed to participate in a survey being conducted by park employees. Find the experimental probability that an amusement park visitor will participate in the survey. P(participation) # of successes # of trials ou could expect 1 out of every 5 people to participate in the survey. Or there is a % chance of a visitor participating in the survey. Sally rolled a die 1 times and the results are shown below. Use this information to answer the following questions. # on Die Picture of oll esults 5 fives 1

2 Experimental and.notebook 1 hat is the experimental probability of rolling a 5? hat is the experimental probability of rolling a? # on Die Picture of oll esults # on Die Picture of oll esults 5/ 5/ C /5 D /5 C D / 5 fives 5 fives 3 ased on the experimental probability you found, if you rolled the die 1 times, how many sixes would you expect to get? A C D 6 sizes 1 sixes 1 sixes 6 sixes # on Die Picture of oll esults 5 fives Mike flipped a coin 15 times and it landed on tails 11 times. hat is the experimental probability of landing on heads? hat is the theoretical probability of spinning green? of an event number of favorable outcomes total number of possible outcomes FAI

3 Experimental and.notebook Example 1 Marbles Find the probability of randomly choosing a white marble from the marbles shown. Example Marbles Suppose you randomly choose a gray marble. Find the probability of this event. P(white) 1 5 P(gray) 3 1 There is a in 5 chance of picking a white marble or a % possibility. There is a 3 in 1 chance of picking a gray marble or a 3% possibility. Example 3 Coins Find the probability of getting tails when you flip a coin. P(tails) There is a 1 in chance of getting tails when you flip a coin or a 5% possibility. 1 5 hat is the theoretical probability of picking a green marble? 7/8 6 hat is the theoretical probability of picking a black marble? 7 hat is the theoretical probability of picking a white marble? 7/8 D 7/8 C 1/ 3

4 Experimental and.notebook 8 hat is the theoretical probability of not picking a white marble? A 3/ 7/8 9 hat is the theoretical probability of rolling a three? 3 1 hat is the theoretical probability of rolling an odd number? 3 11 hat is the theoretical probability of rolling a number less than 5? A /3 1 hat is the theoretical probability of not rolling a? A /3 13 Seth tossed a fair coin five times and got five heads. The probability that the next toss will be a tail is A C D From the New ork State Education Department. Office of Assessment Policy, Development and Administration. Internet. Available from accessed 17, June, 11.

5 Experimental and.notebook 1 hich inequality represents the probability, x, of any event happening? 15 The spinner shown is divided into 8 equal sections. A x < x < 1 C x < 1 D x 1 The arrow on this spinner is spun once. hat is the probability that the arrow will land on a section labeled with a number greater than 3? From the New ork State Education Department. Office of Assessment Policy, Development and Administration. Internet. Available from accessed 17, June, 11 Enter only your fraction. From PACC sample test 16 eagan will use a random number generator 1, times. Each result will be a digit form 1 to 6. hich statement best predicts how many times the digit 5 will appear among the 1, results? A It will appear exactly times. It will appear close to times but probably not exactly times. Class Activity Each student flips a coin 1 times and records the number of heads and the number of tail outcomes. Each student calculates the experimental probability of flipping a tail and flipping a head. Use the experimental probabilities determined by each student to calculate the entire class's experimental probability for flipping a head and flipping a tail. C It will appear exactly times. D It will appear close to times but probably not exactly times. From PACC sample test the following: hat is the theoretical probability for flipping a tail? A head? Compare the experimental probability to the theoretical probability for 1 experiments. Compare the experimental probability to the theoretical probability when the experiments for all of the students are considered? 5