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Section 9-1 Determining Probabilities 511 20. Ateacher has a jar that contains his students' names: 21. The experimental probability of rolling a 6 on a single die Maria, Jenna, Boyd, Melinda, Brett, Jacob, Jasper, Tara, Colleen, was obtained by rolling the die 100 times and obtaining 16 Juan. If he draws one name at random, find the probability 6s. What is the numerical difference between this probabil- of the following events. ity and the theoretical probability of rolling a 6 when the a. 4-letter name die is tossed once? b. 5-letter name 22. How many times would you expect to obtain a 6 on a roll c. 7-letter name of a die if you rolled it 1000 times? d. Name starting with M e. Name starting with B or J f. Name ending with a Mathematical Connections 9-1 1. Explain whether you think that when calling a seven-digit 10. Zoe is playing a game in which she draws one ball from phone number without its area code, each digit 0-9 has an one of the boxes shown. She wins if she draws a white equal chance of being chosen as the lead number. ball from either box #1 or box #2. She says that in order to 2. Events A and B are from the same sample space, and maximize her chances of winning she will always pick box P(A) = 0.8 and P(B) = 0.9. Explain whether events A #2 because it has more white balls. Is she correct? Why? and B can be mutually exclusive. 3. Rhea says that when she shoots a free throw in basketball, oooo oooooo0. she will either make it or miss it. Because there are only two outcomes and one of them is making a basket, Rhea #1 #2 11. Ian and Sophia flip a fair coin ten times and record their claims the probability of her making a free throw is ?. results; they find that the coin landed on heads eight Explain whether Rhea's reasoning is correct. times. Ian says, "This means the coin will land on heads 4. Consider a page of a newspaper as a sample of letters in 80% of the time!" Sophia says, "I don't think so; if we flip the English language, and choose one letter at random. it many more times, our results should be closer to it land- Which letter do you expect to have the highest probability ing on heads about 50% of the time." Who is right? How of being chosen? Why? do you know? 5. If a fair die is thrown 1000 times and a 6 appears on each 12. A certain game has four mutually exclusive outcomes: toss, explain whether you believe the die is fair. 6. List three real-world situations that do not involve Outcome A has probability 5/16. weather or gambling where probability might be used. Outcome B has probability 1/4. 7. If possible, for each of the following letters, describe an Outcome C has probability 3/8. event that has the approximate probability marked by the letter on the probability line. Outcome D has probability 1/16. Carlos says, "These probabilities are low; there must be more than four outcomes for this game!" What would you say to help him understand? Probability Line 13. A student claims that if a fair coin is tossed and comes up heads 5 times in a row, then, according to the law of aver- Connecting Mathematics to the Classroom ages, the probability of tails on the next toss is greater than 8. Mari argues that if one chooses a page at random from the probability of heads. What is your reply? a typical English language dictionary, the probability of 14. A student observes the following spinner and claims that choosing a page with words that begin with the letter Q is the color red has the highest probability of appearing since there are two red areas on the spinner. What is your 26 because there are 26 letters in the alphabet. How might reply? you respond? Blue 9. Jose claims that if the following spinner is spun 100 times, Red Red the number 4 will occur most often because the greatest area of the spinner is covered by the number 4. What would you tell Jose about his conjecture? What is the prob- Green ability that a 4 will occur on any spin? 15. A student tosses a coin 3 times, and a head appears each time. The student concludes that the coin is not fair. What is your response? 16. A student wonders why probabilities cannot be negative. What is your response?Discussion Topic (2 Please read the following and answer the questions bellow. You must answer all the questions and respond to at least one peer to receive full credit. Replies to peers such as: I agree and good point with out details or examples will not be accepted. This is taken from you textbook Section 9.1 page 511 number 16. A student wonders why probabilities cannot be negative. You will need to create a new thread and answer the following: 1. Define the term probability. 2. Give real word examples (two or more) where a solution or situation can yield a negative number. (Non- Probability Examples) 3. Give real word examples (two or more) where a solution or situation cannot yield a negative number. (Non- Probability Examples) A student wonders why probabilities cannot be negative. (Taken from pg 511 of your textbook) 4. Write an explanation to your student that answers their question as to why probabilities cannot be negative. Remember that you are going to be a future teacher. When you answer this questions use images, activities or lessons that you have found or think would be good to use in your future classroom. Use the knowledge you have from other education classes on how different students learn and use those skills to answer the students