Defining and Representing Probabilitybfunderburkstms.weebly.com/uploads/2/2/8/3/... · Brett received the following dart board for his birthday. The rule book says that two darts

Chapter 16 Assignments • 293

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Lesson 16.1 Assignment

Name ________________________________________________________ Date _________________________

Rolling, Rolling, Rolling . . .Defining and Representing Probability

1. Rasheed is getting dressed in the dark. He reaches into his sock drawer to get a pair of socks.

He knows that his sock drawer contains six pairs of socks, and each pair is a different color.

Each pair of socks is folded together. The pairs of socks in the drawer are red, brown, green,

white, black, and blue.

a. How many possible outcomes are there in the experiment?

b. What are the possible outcomes of the experiment?

c. List the sample space for the experiment.

d. Calculate the probability that Rasheed will choose a pair of blue socks, or P(blue).

e. Calculate the probability that Rasheed will choose a pair of green socks, or P(green).

f. Calculate the probability that Rasheed will choose a pair of socks that are not red, or P(not red).

g. Calculate the probability that Rasheed will choose a pair of purple socks, or P(purple).

294 • Chapter 16 Assignments

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Lesson 16.1 Assignment page 2

2. Consider the following bag containing seven marbles, each with a number written on it.

An experiment consists of reaching into the bag and drawing a marble.

1 2

3

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67




d. Calculate the probability of drawing the marble with the number 2 from the bag, or P(2).

e. Calculate the probability of drawing a marble with an odd number from the bag, or P(odd).

f. Calculate the probability of drawing a marble not containing the number 5 from the bag, or

P(not 5).

g. Calculate the probability of drawing a marble with the number 1, 2, 3, 4, 5, 6, or 7 from the bag,

or P(1, 2, 3, 4, 5, 6, or 7).

7718A_C2_Assign_CH16_293-314.indd 294 6/14/11 10:09 AM


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Name ________________________________________________________ Date _________________________

3. Consider the square spinner shown and assume all sectors are the same size. An experiment

consists of spinning the spinner one time.

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d. Calculate the probability that the spinner stops on the sector with the letter q, or P(q).

e. Calculate the probability that the spinner stops on a sector with a number, or P(number).

f. Calculate the probability that the spinner stops on a sector with a number greater than 10,

or P(number greater than 10).

g. Calculate the probability that the spinner stops on a sector with a number less than 2, or

P(number smaller than 2).



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4. Determine whether each event is certain to occur, just as likely to occur as not to occur, or

impossible to occur. Then write the probability.

a. A coin is flipped and the coin lands heads up. Express the probability as a fraction.

b. Tuesday follows Monday in the week. Express the probability as a percent.

c. You have only white shirts in your closet. Express the probability of reaching into your closet

and choosing a red shirt as a fraction.

d. A box contains 2 green balls and 2 yellow balls. You reach into the box and grab a yellow ball.

Express the probability as a decimal.

5. A box contains 2 black buttons, 2 white buttons, and 2 pink buttons. One button is drawn from the

box at a time.

a. List the sample space for the experiment.

b. Calculate P(black).



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Name ________________________________________________________ Date _________________________

c. Calculate P(white).

d. Calculate P(pink).

e. What do you notice about all of the probabilities you calculated in parts (b) through (d)?

g. Determine the sum of all of the probabilities from parts (b) through (d).


box at a time.

a. Calculate P(black).

b. Calculate P(white).

c. Calculate P(pink).

d. What do you notice about all of the probabilities you calculated in parts (a) through (c)?

e. Determine the sum of all of the probabilities from parts (a) through (c).



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box at a time.

a. Calculate P(black).

b. Calculate P(white).

c. Calculate P(pink).

d. Are the probabilities equal? Explain your reasoning.

e. Determine the sum of all of the probabilities from parts (a) through (c).



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Name ________________________________________________________ Date _________________________

Toss the CupDetermining Experimental Probability

1. A tetrahedron is a four-sided solid, as shown. The faces of a tetrahedron are identical triangles.

The number 1 is written on one face of the tetrahedron, the number 2 is written on a second face

of the tetrahedron, the number 3 is written on a third face of the tetrahedron, and the number 4 is

written on the fourth face of the tetrahedron. Suppose that you roll the tetrahedron 40 times.

a. List the sample space.

b. How many times do you expect the tetrahedron to show each of the four sides?

c. Determine P(1), P(2), P(3), and P(4). Explain your calculations.


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d. Suppose that you rolled the tetrahedron 40 times and recorded the results shown in the table.

Complete the table by determining the totals and the experimental probabilities.

Number Tally TotalExperimental Probability

1 |||| ||||

2 |||| |||| |

3 |||| |||| ||

4 |||| |||

e. Compare the experimental probabilities you calculated in part (d) to the probabilities you

calculated in part (c). Are they the same or different? Why?


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Name ________________________________________________________ Date _________________________

2. Alfonso plays a game of bean bag toss by tossing a bean bag onto a large plastic mat with a large

rectangle divided up into three smaller rectangles, as shown in the figure.

A B C

a. If Alfonso tosses the bean bag, in which rectangle does it have the best chance of landing?

the least chance?

b. Predict P(A), P(B), and P(C).

c. Is there a way to determine the exact probabilities of landing on each of the rectangles?

Explain your reasoning.


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d. Alfonso plays the game by tossing the beanbag 40 times. His results are shown in the following

table. Complete the table.

Letter Tally TotalExperimental Probability

A |||| |||| |||| |||| ||

B |||| |||

C |||| ||||

e. If Alfonso plays the game again, do you think he will get the same results? Explain.

f. Suppose the probabilities for the different rectangles are known to be:

P(A) 5 1 __ 2 P(B) 5 3 ___

10 P(C) 5 1 __

5

If Alfonso tosses the bean bag 50 times, predict the number of times the bean bag would land

on each rectangle.


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Double Your FunDetermining Theoretical Probability

1. Brett received the following dart board for his birthday. The rule book says that two darts are

to be thrown and that individual’s score is the sum of the two numbers.

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a. List the sample space.

b. Are all outcomes equally likely? Explain your reasoning.

c. Complete the number array to determine all the possibilities for obtaining the sums.

Dart 1

Dart

2

1 2 4 6 8

2

4

6

8


Name ________________________________________________________ Date _________________________


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d. How many possibilities are in the number array?

e. Use the number array to help complete the tally table to determine the number of times each

sum appears.

Sum Tally

4

6

8

10

12

14

16

f. Calculate the theoretical probabilities for each sum.

P(4) 5 P(10) 5

P(6) 5 P(12) 5

P(8) 5 P(14) 5

P(16) 5


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Name ________________________________________________________ Date _________________________

g. Calculate each probability.

P(sum even) 5

P(sum greater than 8) 5

P(sum odd) 5

2 If two darts are thrown 80 times, how many times do you predict each of the following sums

would occur?

a. 8

b. 10

c. 14


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3. Determine if each probability can be determined experimentally, theoretically, or both.

Explain your reasoning.

a. Humans will land on Mars in the next 10 years.

b. A number cube is rolled two times and the product of the two numbers is recorded.

c. A box contains red, white, and blue marbles and you are not allowed to look inside the box. You

reach in and grab a blue marble.

d. A coin is tossed ten times and the results are recorded.

e. The next car to pass you will be silver in color.


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A Toss of a CoinSimulating Experiments

1. Milton’s dad likes to change the family computer’s password every day. Milton is allowed to use

the computer on Saturdays if he completes his homework and is able to choose the correct

password. Every Saturday, Milton receives 3 sealed envelopes, each containing a password.

Only one password is correct, and he is only allowed to choose one envelope. Suppose that this

upcoming Saturday is the first of four Saturdays of this month.

a. Estimate the number of times Milton will be able to use the computer this month by guessing.

b. One model that you could use to simulate this problem situation is to choose 3 cards from a

deck of cards. Suppose you choose the ace of spades (black), the ace of clubs (black), and the

ace of diamonds (red). Shuffle the 3 cards and place them on a table face down. Draw a card.

You win if you draw the ace of diamonds; otherwise you lose. What is the probability of drawing

the ace of diamonds?

c. Explain how the card method in part (b) simulates Milton’s situation.

d. Describe one trial of the experiment using the card method in part (b) if you want to simulate

Milton’s situation during the month.


Name ________________________________________________________ Date _________________________


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e. Will one trial provide a good estimate of how many times Milton will get to use the family

computer? Explain.

f. Conduct 30 trials of the simulation using the card method described in part (b). Record your

results in the table.

Trial NumberNumber of Successes

Trail NumberNumber of Successes

1 16

2 17

3 18

4 19

5 20

6 21

7 22

8 23

9 24

10 25

11 26

12 27

13 28

14 29

15 30


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Name ________________________________________________________ Date _________________________

g. Graph your results on the dot plot.

0 1 2 3 4

Number of Ace of Diamonds

h. According to your simulation, about how many times should Milton expect to use the family

computer during the month?

2. Describe a simulation to model each situation, and then describe one trial.

a. When playing a certain video game, the rules require you to answer 5 true/false questions

correctly simply by guessing.

b. A box of yogurt-covered dried fruit contains equal amounts of 6 different kinds of dried fruit.

You like only one of the 6 types and claim you can always pick what you like from the box

correctly. To the unaided eye, however, all 6 different kinds of yogurt-covered dried fruit look alike.


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Roll the Cubes AgainUsing Technology for Simulations

1. Milton is only allowed to use the family computer on Saturdays providing he knows the password

to the system for that day. Each Saturday, Milton’s dad gives him 3 new sealed envelopes

containing one password each. Only one of the passwords is correct, and he is only allowed to

choose one of the envelopes. Simulate how many times you expect Milton to be able to use the

computer in one month that has four Saturdays. A simulation for Milton’s situation can be designed

using a computer spreadsheet.

a. Describe one trial.

b. Since there are 4 Saturdays in the month, use 4 columns in the first row of a spreadsheet to

simulate one trial of choosing an envelope containing a password. Type the formula

5 RANDBETWEEN(1,3) in cell A1 and fill right to cell D1. Let the number 1 represent Milton

choosing the password that works and the numbers 2 and 3 represent Milton choosing the

passwords that do not work. List and interpret the results of your first trial.


Name ________________________________________________________ Date _________________________


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c. Highlight the first row and then fill down through row 30. What does filling down through

row 30 represent?

d. Record your results in the table.

Trial NumberNumber Correct

Trial NumberNumber Correct

1 16

2 17

3 18

4 19

5 20

6 21

7 22

8 23

9 24

10 25

11 26

12 27

13 28

14 29

15 30


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Name ________________________________________________________ Date _________________________

e. Record your results on the dot plot.

0 1 2 3 4

Number of Correct Passwords Chosen

f. What is the experimental probability of Milton using the family computer on Saturdays?


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g. Is it likely that Milton will get to use the family computer on more than 2 Saturdays? Explain.

h. If Milton runs more trials, is it likely that the experimental probabilities will be closer to the

theoretical probabilities? Explain.

Documents

Defining and Representing Probabilitybfunderburkstms.weebly.com/uploads/2/2/8/3/... · Brett received the following dart board for his birthday. The rule book says that two darts