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@ E] mycourses.rit.edu/d2l/commc i/, Download Elementary Statistics Lab 5: Probability Name: Due: GOALS FOR LAB 5 To explore the understanding of theoretical probability and experimental probability. THEORETICAL PROBABILITY vs. EXPERIMENTAL PROBABILITY Probability The measure of how likely it is for an event to occur. The probability of an event is always a number from O to 1. Theoretical Probability The chances of events happening are determined by calculating results that would occur under ideal circumstances. cant ' s s' For example, let's use a die. Under ideal circumstances, we can define all possible outcomes: A. What is the probability of rolling a '4' on a die? (fraction) (3 significant digits) B. What is the probability of rolling a '2' on a die? (3 significant digits) Page 1 of 11 Elementary Statistics Lab 5: Probability A. We can say that each face of die has an equal chance to turn up after rolling a die, because the probability is the same for each one. We just figured out the probability without doing an experiment to get the result. This is called theoretical probability. Experimental Probability The chances of something happening, are based on repeated testing and observing results. It is the ratio of the number of times an event occurred to the number of times tested. For example, let's use a die again. Each of you will roll a die 5 times. Count the number of time you get a '4", What is the probability of rolling a '4' on a die? (fraction) (3 significant digits) Is your answer is the same as the theoretical probability? Is your answer greater or less than the theoretical probability? @ E] mycourses.rit.edu/d2l/commc i/, Download times an event occurred to the number of times tested. For example, let's use a die again. Each of you will roll a die 5 times. Count the number of time you get a '4", A. What is the probability of rolling a '4' on a die? (fraction) (3 significant digits) Is your answer is the same as the theoretical probability? Is your answer greater or less than the theoretical probability? Add up all of the student's experiments together since we do not want to roll that many experiments at one time. How many '4's? Total: What is the probability of rolling a '4' on a die? (fraction) (3 significant digits) Page 2 of 11 Elementary Statistics Lab 5: Probability Observation: The more you roll a die to get a '4", say 500 times, the experimental probability will be close to or equal to theoretical probability. This is where the law of large number comes in. EXERCISE 1: ROLLING TWO DICE A. What is the sample space for rolling two dice? Possible Outcomes for Rolling 2 Dice 1.1 2,1 6,1 2 3 7 3 1,6 7 B. What is the total number of possible outcomes? C. What is the theoretical probability for getting the total of 10? (fraction & 3 significant digits) Page 3 of 11 @ E] mycourses.rit.edu/d2l/commc i/, Download Elementary Statistics Lab 5: Probability D. Do an experiment. Roll two dice 5 times and count the number of times you get the total of 10. What is the experimental probability for getting the total of 10? (fraction & 3 significant digits) Add up all of the student's experiments together. How many totals of 10? Total number of experiments: What is the experimental probability? (fraction & 3 significant digits) Compare this experimental probability with the theoretical probability. Rolling two dice, what is the theoretical probability for getting a total of 62 (fraction & 3 significant digits) Rolling one die, what is the theoretical probability for getting 6 dots? (fraction & 3 significant digits) Rolling two dice, what total number has the greatest theoretical probability? Explain your answer. Page 4 of 11 Elementary Statistics Lab 5: Probability I. Rolling one die, how many dots have the greatest theoretical probability? Explain your answer., EXERCISE 2: A PACKET OF M&M PLAIN CANDIES You will use a packet of M&M candies to list the possible outcomes and then compute probability of each color. A. Count each color of M&M candies and record them below. After you count them, you are welcomed to eat them or give them to your friend. There is a good chance that the other student would not have the same result as yours. Color Red |Yellow Green | Blue Orange|Brown Count Probability What is the total number of M&M candies? @ E] mycourses.rit.edu/d2l/commc i/, Download B. What is the total number of M&M candies? C. Complete the table by finding probability for each color. Round answer to 3 significant digits (no fraction). Page 5 of 11 Elementary Statistics Lab 5: Probability If a M&M candy is randomly selected from the packet, (Write your answer in 3 significant digits) D. What is the probability of getting a yellow candy? What is the probability of getting a purple candy? What is the probability of getting a yellow or an orange candy? SHOW HOW What is the probability of not getting a yellow candy? SHOW HOW If two M&M candies are randomly selected without replacement from the packet, (SHOW HOW and write answer in 3 significant digits) H. What is the probability that they are both red? What is the probability that one candy is blue and the other is brown? Page 6 of 11 Elementary Statistics Lab 5: Probability J. What is the probability that both candies are not orange? If two M&M candies are randomly selected with replacement from the packet, (SHOW HOW and write answer in 3 significant digits) @ E] mycourses.rit.edu/d2l/commc i/, Download Elementary Statistics Lab 5: Probability J. What is the probability that both candies are not orange? If two M&M candies are randomly selected with replacement from the packet, (SHOW HOW and write answer in 3 significant digits) K. What is the probability that they are both red? L. What is the probability that one candy is blue and the other is brown? M. What is the probability that both candies are not orange? Complete the table of ALL packets of M&M candies: Write each probability in 3 significant digits. Color Red IYeIIow Green | Blue Orange' Brown Count | Probability | N. What is the total number of M&M candies? Page 7 of 11 Elementary Statistics Lab 5: Probability The candies from all of the packets are in an imaginary bowl. If three M&M candies are selected without replacement at random from the bowl, (SHOW HOW and write answer in 3 significant digits) P. What is the probability that they are all green? Q. What is the probability that the first two candies are yellow and the third one is red? If three M&M candies are selected with replacement at random from the bowl, (SHOW HOW and write answer in 3 significant digits) R. What is the probability that they are all green? S. What is the probability that the first two candies are yellow and the third one is red? @ E] mycourses.rit.edu/d2l/commc i/, Download If ten M&M candies are selected with replacement at random from the bowl, (SHOW HOW and write answer in 3 significant digits) T. What is the probability that they are all brown? Page 8 of 11 Elementary Statistics Lab 5: Probability EXERCISE 3: A DECK OF CARDS A deck of cards contains the following possible outcomes shown below. The shapes of Heart and Diamond are red, and the Spade and Club are black. Aw Aa A Ke Ka K Qa Ja A. What is the total number of cards? If a card is drawn at random from the deck, (Write your answer both in fraction and probability with 3 significant digits) B. What is the probability of getting a King? Is this a theoretical or experimental probability? What is the probability of getting a Diamond? What is the probability of getting a red shape? Page 9 of 11 Elementary Statistics Lab 5: Probability E. What is the probability of getting a red or black shape? What is the probability of getting a 2 or a Jack? What is the probability of getting a Queen of Hearts? H. What is the probability of not getting a Club? @ E] mycourses.rit.edu/d2l/commc i/, Download Elementary Statistics Lab 5: Probability E. What is the probability of getting a red or black shape? What is the probability of getting a 2 or a Jack? G. What is the probability of getting a Queen of Hearts? H. What is the probability of not getting a Club? What is the probability of getting a 4, 6, 8 or 10? If two cards are drawn randomly with replacement from the deck, (SHOW HOW and write answer in 3 significant digits) J. What is the probability of getting both Queens? K. What is the probability of getting both Hearts? Page 10 of 11 Elementary Statistics Lab 5: Probability If two cards are drawn randomly without replacement from the deck, (SHOW HOW and write answer in 3 significant digits) L. What is the probability of getting a Jack and then a ten? ___ M. What is the probability of getting both cards not Spades? If five cards are drawn randomly without replacement from the deck, (SHOW HOW and write answer in 3 significant digits) N. What is the probability of getting a full house such as 11J99? @ E] mycourses.rit.edu/d2l/commc i/, Download H. What is the probability of not getting a Club? What is the probability of getting a 4, 6, 8 or 10? If two cards are drawn randomly with replacement from the deck, (SHOW HOW and write answer in 3 significant digits) J. What is the probability of getting both Queens? K. What is the probability of getting both Hearts? Page 10 of 11 Elementary Statistics Lab 5: Probability If two cards are drawn randomly without replacement from the deck, (SHOW HOW and write answer in 3 significant digits) L. What is the probability of getting a Jack and then a ten? ___ M. What is the probability of getting both cards not Spades? If five cards are drawn randomly without replacement from the deck, (SHOW HOW and write answer in 3 significant digits) N. What is the probability of getting a full house such as 111997 Page 11 of 11