Name: Date: Hour : Classical vs. Empirical Probability Activity (100 Formative Points) For this activity, you will be taking part in 5 different probability experiments: Rolling dice, drawing cards, drawing Scrabble letters from a bag, flipping coins, and PLINKO. You may work with other people, but everyone MUST turn in their own packet. For each experiment you will be asked to FIRST calculate different classical probabilities, and then you will perform the experiment described and compute the approximate EMPIRICAL probabilities based on your results. You may work through the stations in any order that you wish. There is only one PLINKO board and one bag of Scrabble letters available; but there are plenty of dice, cards, and coins for more than one group to use at a time. STATION 1: FLIPPING COINS 1. Define the SAMPLE SPACE for flipping one coin. 2. Calculate the CLASSICAL probability for each outcome in the sample space. Flip a coin 15 times and record your results in the following table. Outcome Tally Frequency Heads Tails Using the EMPIRICAL method calculate the following approximate probabilities. 1. P(Heads) = 2. P(E) where E = getting a tails 3. How do the empirical probabilities compare to the classical probabilities?
STATION 2: DRAWING LETTERS FROM A BAG The bag at this station has 26 tiles in it (1 tile for each letter in the alphabet). 1. Define the Event = Drawing a vowel 2. Define the Event = Drawing a letter that is in DATA ANALYSIS 3. Calculate the CLASSICAL probability of drawing a vowel. 4. Calculate P(A, B, or C) 5. Calculate P(E) where E = {A, D, I, N, S, T, Y} 6. Define the Event = Drawing a letter in YOUR first or last name 7. Calculate P(E) where E is the event from #6 Draw ONE letter from the bag 20 times and complete the table. Be sure to REPLACE THE LETTER BEFORE DRAWING ANOTHER ONE. (i.e. draw one letter, record, put it back; draw a second letter, etc.) Letter Frequency Letter Frequency Letter Frequency Letter Frequency A H O V B I P W C J Q X D K R Y E L S Z F M T G N U
Use the empirical method to calculate the approximate probability for each of the following based on the table you just filled out on the previous page. 1. Calculate the empirical probability of drawing a vowel. 2. Use the empirical method to calculate P(A, B, or C). 3. Given that E = {A, D, I, N, S, T, Y} 4. Given that E = Picking a letter that is in YOUR first or last name calculate P(E). 5. How do these empirical probabilities compare to the classical probabilities you calculated prior to conducting the experiment? STATION 3: PLINKO 1. How many places can the disk land? 2. How many different colors can the disk land on? 3. Define the sample space of dropping one disk down the PLINKO board. 4. Define the event of having the disk land on red or yellow. 5. Calculate the CLASSICAL probabilities for each outcome in the sample space. (Assume each color is equally likely to occur.) 6. Calculate P(E), where E = Landing on yellow or red 7. Given that E = landing on a blue, yellow, or green; calculate P(E).
Drop a disk 15 different times on the PLINKO board and record your data in the table below. Color Tally Frequency White Blue Green Yellow Red Use the EMPIRICAL method to approximate the following probabilities. 1. Approximate the probability of each outcome in the sample space. 2. Using the empirical method, find P(E) if E = Landing on a yellow or red 3. Use the empirical method. Given that E = {Blue, Yellow, Green}, calculate P(E). 4. How do the empirical probabilities that you just calculated compare to the classical probabilities you calculated prior to the experiment? 5. Based on these probabilities, would you say that all colors have the SAME probability or are equally likely to occur? Why or why not?
STATION 4: ROLLING DICE PART 1: ROLLING 1 DIE 1. Define the sample space of rolling one die. 2. Define the event = Rolling an odd number 3. Determine the CLASSICAL probability for each outcome in the sample space. 4. Determine the CLASSICAL probability of rolling an odd number. 5. If E = {2, 4, 6}, determine P(E). Roll ONE die 15 times and record your results in the table below. Number Rolled Tally Frequency 1 2 3 4 5 6 Using an EMPIRICAL approach, approximate the following probabilities. 1. Approximate the probabilities for each possible outcome in the sample space. 2. Given that E = {1, 2, 5}, calculate P(E) using the empirical method. 3. Find the empirical probability of rolling an odd number. 4. How do the empirical probabilities compare to the classical probabilities?
PART 2: ROLLING TWO DICE 1. Define the sample space for rolling TWO dice. (All possible combinations. Hint: there are 36. One more hint: 1,2 IS DIFFERENT THAN 2,1) 2. Define the Event = Sum of 5 3. Define the Event = Sum of 8 4. Calculate the CLASSICAL probability for rolling two dice whose sum is 5. 5. Given that Event = Sum of 8, calculate P(E). Roll TWO dice at once, 15 times. Add the two numbers together to get the sum, and record your data in the table below. Sum Frequency Sum Frequency Sum Frequency 2 6 10 3 7 11 4 8 12 5 9 Use the EMPIRICAL method to calculate the following approximate probabilities. 1. Approximate the probability of rolling 2 dice whose sum is 5. 2. Given that E = sum of 8, calculate P(E) using the empirical method. 3. How do your empirical probabilities that you just calculated compare to the classical probabilities that you calculated prior running the experiment.
STATION 5: DRAWING CARDS GETTING TO KNOW A DECK OF CARDS 1. How many possible outcomes are there when drawing ONE card? 2. How many different suits (symbols) are there? 3. How many cards are in each suit? 4. How many of each card VALUE are there? (i.e. how many 4 s, how many King s, etc.) 5. How many cards of each color are there? CLASSICAL PROBABILITY 1. What is the probability of drawing a red card? 2. Given that E = drawing a diamond, calculate P(E) using the CLASSICAL method. 3. Calculate P(Face card). (Face cards are Kings, Queens, and Jacks) 4. What is the CLASSICAL probability of drawing an ace? 5. Calculate P(E) if E = 9 6. What is the CLASSICAL probability of drawing any one individual card from a standard deck of cards?
Draw ONE card at a time, 25 times. BE SURE TO PUT EACH CARD BACK INTO THE DECK BEFORE DRAWING YOUR NEXT CARD. Record your data in the table below. Ace 2 3 4 5 6 7 8 9 10 Jack Queen King HEARTS DIAMONDS CLUBS SPADES Use the EMPIRICAL method to approximate the following. 1. Given that E = Drawing a red card, calculate P(E) using the EMPIRICAL method. 2. Using the EMPIRICAL method, calculate P(Diamond). 3. Use the EMPIRICAL method to calculate P(E) if E = drawing a face card. 4. Given that E = drawing an ace, calculate P(E) using the EMPIRICAL method. 5. Calculate the probability of drawing the 9. 6. How do your empirical probabilities compare to the classical probabilities you calculated before the experiment?