Bernoulli Experiments – Open Ended Intervals Objectives: Determine probability of having <= r or >= r “successes” in n Bernoulli trials. Learn how to compute Binomial probabilities using TI-84. DIRECTIONS: Open your bag of M&M’s. Do NOT eat them! Count the number of M&M’s, and the number red M&Ms. Using the numbers for your bag, the numbers from your group, and the numbers from the “Do Now” problem, fill in the following table: Sample Size of Number of Probability of Sample Red M&Ms getting Red Do Now 913 102 Group Your Bag Put your M&M’s in a ziplock bag. (You can take them with you and eat later… not in class). According to mms.com, the actual probability of getting a red M&M is 0.13. Working as a team, and using this value for p, complete the following worksheet and answer the questions. Hint: How can you use your technology effectively?

Use the Binomial Probability to compute the probability of getting exactly r red M&M’s in a bag of 21. Prob(r reds) = (nCr) p r q n-r What value do you use for n, p, and q? Number of Red M&M’s r Probability 11 1 12 2 13 3 14 4 15 5 16 6 17 7 18 8 19 9 20 10 21

Questions What is the probability of getting at most 2 red M&M’s in a new bag? What is the probability of getting at least 6 red M&M’s in a new bag? What is the probability of getting 3-5 red M&M’s in a new bag? Open 2 new bags for your groups, and write down the number of red M&M’s in each. How do the numbers agree with the predictions made on the previous page and above?

Homework 1. Suppose Wheaties Cereal gives a card of a sports star in each box. Suppose that Tiger Woods is in 20% of the boxes. Assume there are 10 boxes of Wheaties on your supermarket’s shelf. Graph the probability of finding exactly 0, 1, 2, … 10 pictures of Tiger in these boxes. the probability of getting at least 1, 2, 3, … 10 pictures of Tiger. the probability of getting at most 1, 2, … 9 pictures of Tiger. 2. How can you use the TI-83/84 to display the values of a Binomial pdf and cdf side-by-side? 3. Graph the values of Binompdf for n=25, p=-.45, and r ranging from 5 to 20. What does the shape of the curve look like?

Bernoulli Experiments – Open Ended Intervals OBJECTIVES: Determine probability of having <= r or >= r “successes” in n Bernoulli trials. Learn how to compute Binomial probabilities using TI-84. DIRECTIONS: Open your bag of M&M’s. Do NOT eat them! Count the number of M&M’s, and the number yellow M&Ms. Using the numbers for your bag, the numbers from your group, and the numbers from the “Do Now” problem, fill in the following table: Sample Size of Number of Probability of Sample Yellow M&Ms getting Yellow Do Now 913 127 Group Your Bag Put your M&M’s in a ziplock bag. (You can take them with you and eat later… not in class). According to mms.com, the actual probability of getting a yellow M&M is 0.14. Working as a team, and using this value for p, complete the following worksheet and answer the questions. Hint: How can you use your technology effectively?

Use the Binomial Probability to compute the probability of getting exactly r yellow M&M’s in a bag of 21. Prob(r yellows) = (nCr) p r q n-r What value do you use for n, p, and q? Number of Yellow M&M’s r Probability 11 1 12 2 13 3 14 4 15 5 16 6 17 7 18 8 19 9 20 10 21

Questions What is the probability of getting at most 2 yellow M&M’s in a new bag? What is the the probability of getting at least 6 yellow M&M’s in a new bag? What is the probability of getting 3-5 yellow M&M’s in a new bag? Open 2 new bags for your groups, and write down the number of yellow M&M’s in each. How do the numbers agree with the predictions made on the previous page and above?

Homework 1. Suppose Wheaties Cereal gives a card of a sports star in each box. Suppose that Tiger Woods is in 20% of the boxes. Assume there are 10 boxes of Wheaties on your supermarket’s shelf. Graph the probability of finding exactly 0, 1, 2, … 10 pictures of Tiger in these boxes. the probability of getting at least 1, 2, 3, … 10 pictures of Tiger. the probability of getting at most 1, 2, … 9 pictures of Tiger. 2. How can you use the TI-83/84 to display the values of a Binomial pdf and cdf side-by-side? 3. Graph the values of Binompdf for n=20, p=-.45, and r ranging from 0 to 20. What does the shape of the curve look like?

Bernoulli Experiments – Open Ended Intervals OBJECTIVES: Determine probability of having <= r or >= r “successes” in n Bernoulli trials. Learn how to compute Binomial probabilities using TI-84. DIRECTIONS: Open your bag of M&M’s. Do NOT eat them! Count the number of M&M’s, and the number orange M&Ms. Using the numbers for your bag, the numbers from your group, and the numbers from the “Do Now” problem, fill in the following table: Sample Size of Number of Probability of Sample Orange M&Ms getting Orange Do Now 913 197 Group Your Bag Put your M&M’s in a ziplock bag. (You can take them with you and eat later… not in class). According to mms.com, the actual probability of getting a orange M&M is 0.20. Working as a team, and using this value for p, complete the following worksheet and answer the questions. Hint: How can you use your technology effectively?

Use the Binomial Probability to compute the probability of getting exactly r orange M&M’s in a bag of 21. Prob(r oranges) = (nCr) p r q n-r What value do you use for n, p, and q? Number of Orange M&M’s r Probability 11 1 12 2 13 3 14 4 15 5 16 6 17 7 18 8 19 9 20 10 21

Questions What is the probability of getting at most 2 orange M&M’s in a new bag? What is the probability of getting at least 6 orange M&M’s in a new bag? What is the probability of getting 3-5 orange M&M’s in a new bag? Open 2 new bags for your groups, and write down the number of orange M&M’s in each. How do the numbers agree with the predictions made on the previous page and above?

Homework 1. Suppose Wheaties Cereal gives a card of a sports star in each box. Suppose that Tiger Woods is in 20% of the boxes. Assume there are 10 boxes of Wheaties on your supermarket’s shelf. Graph the probability of finding exactly 0, 1, 2, … 10 pictures of Tiger in these boxes. the probability of getting at least 1, 2, 3, … 10 pictures of Tiger. the probability of getting at most 1, 2, … 9 pictures of Tiger. 2. How can you use the TI-83/84 to display the values of a Binomial pdf and cdf side-by-side? 3. Graph the values of Binompdf for n=20, p=-.45, and r ranging from 0 to 20. What does the shape of the curve look like?

Bernoulli Experiments – Open Ended Intervals OBJECTIVES: Determine probability of having <= r or >= r “successes” in n Bernoulli trials. Learn how to compute Binomial probabilities using TI-84. DIRECTIONS: Open your bag of M&M’s. Do NOT eat them! Count the number of M&M’s, and the number green M&Ms. Using the numbers for your bag, the numbers from your group, and the numbers from the “Do Now” problem, fill in the following table: Sample Size of Number of Probability of Sample Green M&Ms getting Green Do Now 913 119 Group Your Bag Put your M&M’s in a ziplock bag. (You can take them with you and eat later… not in class). According to mms.com, the actual probability of getting a green M&M is 0.16. Working as a team, and using this value for p, complete the following worksheet and answer the questions. Hint: How can you use your technology effectively?

Use the Binomial Probability to compute the probability of getting exactly r green M&M’s in a bag of 21. Prob(r greens) = (nCr) p r q n-r What value do you use for n, p, and q? Number of Green M&M’s r Probability Number of Green M&M’s r 11 1 12 2 13 3 14 4 15 5 16 6 17 7 18 8 19 9 20 10 21

Questions What is the probability of getting at most 2 green M&M’s in a new bag? What is the probability of getting at least 6 green M&M’s in a new bag? What is the probability of getting 3-5 green M&M’s in a new bag? Open 2 new bags for your groups, and write down the number of green M&M’s in each. How do the numbers agree with the predictions made on the previous page and above?

Homework 1. Suppose Wheaties Cereal gives a card of a sports star in each box. Suppose that Tiger Woods is in 20% of the boxes. Assume there are 10 boxes of Wheaties on your supermarket’s shelf. Graph the probability of finding exactly 0, 1, 2, … 10 pictures of Tiger in these boxes. the probability of getting at least 1, 2, 3, … 10 pictures of Tiger. the probability of getting at most 1, 2, … 9 pictures of Tiger. 2. How can you use the TI-83/84 to display the values of a Binomial pdf and cdf side-by-side? 3. Graph the values of Binompdf for n=20, p=-.45, and r ranging from 0 to 20. What does the shape of the curve look like?

Bernoulli Experiments – Open Ended Intervals OBJECTIVES: Determine probability of having <= r or >= r “successes” in n Bernoulli trials. Learn how to compute Binomial probabilities using TI-84. DIRECTIONS: Open your bag of M&M’s. Do NOT eat them! Count the number of M&M’s, and the number blue M&Ms. Using the numbers for your bag, the numbers from your group, and the numbers from the “Do Now” problem, fill in the following table: Sample Size of Number of Probability of Sample Blue M&Ms getting Blue Do Now 913 228 Group Your Bag Put your M&M’s in a ziplock bag. (You can take them with you and eat later… not in class). According to mms.com, the actual probability of getting a blue M&M is 0.24. Working as a team, and using this value for p, complete the following worksheet and answer the questions. Hint: How can you use your technology effectively?

Use the Binomial Probability to compute the probability of getting exactly r blue M&M’s in a bag of 21. Prob(r blues) = (nCr) p r q n-r What value do you use for n, p, and q? Number of Blue M&M’s r Probability 11 1 12 2 13 3 14 4 15 5 16 6 17 7 18 8 19 9 20 10 21

Questions What is the probability of getting at most 2 blue M&M’s in a new bag? What is the probability of getting at least 6 blue M&M’s in a new bag? What is the probability of getting 3-5 blue M&M’s in a new bag? Open 2 new bags for your groups, and write down the number of blue M&M’s in each. How do the numbers agree with the predictions made on the previous page and above?

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