Fillable Problems Probability Models Worksheets printable pdf download

1. Bernoulli. Can we use probability models based on Bernoulli trials to investigate the following situations? Explain.

a) We roll 50 dice to find the distribution of the number of spots on the faces.

b) How likely is it that in a group of 120 the majority may have Type A blood, given that Type A is found in 43% of

the population?

c) We deal 5 cards from a deck and get all hearts. How likely is that?

d) We wish to predict the outcome of a vote on the school budget, and poll 500 of the 3000 likely voters to see how

many favor the proposed budget.

e) A company realizes that about 10% of its packages are not being sealed properly. In a case of 24, is it likely that

more than 3 are unsealed?

2. Bernoulli 2. Can we use probability models based on Bernoulli trials to investigate the following situations? Explain.

a) You are rolling 5 dice and need to get at least two 6's to win the game.

b) We record the eye colors found in a group of 500 people.

c) A manufacturer recalls a doll because about 3% have buttons that are not properly attached. Customers return 37

of these dolls to the local toy store. Is the manufacturer likely to find any dangerous buttons?

d) A city council of 11 Republicans and 8 Democrats picks a committee of 4 at random. What's the probability they

choose all Democrats?

e) A 2002 Rutgers University study found that 74% of high-school students have cheated on a test at least once.

Your local high-school principal conducts a survey in homerooms and gets responses that admit to cheating from

322 of the 481 students.

3. Simulating the model. Think about the Tiger Woods picture search again. You are opening boxes of cereal one at a

time looking for his picture, which is in 20% of the boxes. You want to know how many boxes you might have to

open in order to find Tiger.

a) Describe how you would simulate the search for Tiger using random numbers.

b) Run at least 30 trials.

c) Based on your simulation, estimate the probabilities that you might find your first picture of Tiger in the first box,

the second, etc.

d) Calculate the actual probability model.

e) Compare the distribution of outcomes in your simulation to the probability model.

4. Simulation II. You are one space short of winning a child's board game and must roll a 1 on a die to claim victory.

You want to know how many rolls it might take.

a) Describe how you would simulate rolling the die until you get a 1.

b) Run at least 30 trials.

c) Based on your simulation, estimate the probabilities that you might win on the first roll, the second, the third, etc.

d) Calculate the actual probability model.

e) Compare the distribution of outcomes in your simulation to the probability model.

5. Tiger again. Let's take one last look at the Tiger Woods picture search. You know his picture is in 20% of the cereal

boxes. You buy five boxes to see how many pictures of Tiger you might get.

a) Describe how you would simulate the number of pictures of Tiger you might find in five boxes of cereal.

b) Run at least 30 trials.

c) Based on your simulation, estimate the probabilities that you get no pictures of Tiger, 1 picture, 2 pictures, etc.

d) Calculate the actual probability model.

e) Compare the distribution of outcomes in your simulation to the probability model.

6. Seatbelts. Suppose 75% of all drivers always wear their seatbelts. Let's investigate how many of the drivers might be

belted among five cars waiting at a traffic light.

a) Describe how you would simulate the number of seatbelt-wearing drivers among the five cars.

b) Run at least 30 trials.

c) Based on your simulation, estimate the probabilities there are no belted drivers, exactly one, two, etc.

d) Calculate the actual probability model.

e) Compare the distribution of outcomes in your simulation to the probability model.

Problems Probability Models Worksheets

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