7-1
What are the likelihoods of each of these probabilities?
<1/2
0
1
>1/2
1/2
Unlikely
Impossible
Certain
Likely
Neither likely nor unlikely
Fill in the blanks to complete the expression that could be used to predict the number of winners of a game.
P(event)= number of favorable outcomes divided by______________________
which is equal to ________________ divided by the total number of contestants.
Total number of outcomes; total number of winners
How is experimental probability different from theoretical probability?
Experimental is what did happen, theoretical is what should happen
A complete probability model is described by which of the following statements?
a) A list of all possible outcomes in the sample space and their probabilities
b) The actual outcomes of a trial
c) The number of trials conducted
d) The difference between the theoretical and experimental probabilities of all outcomes
How do theoretical probability and experimental probability differ?
theoretical = what should happen
experimental = what did happen
25 volunteers will wear one of 6 blue, 7 green, 8 yellow, and 4 red aprons during an upcoming food drive. If the aprons are assigned randomly, what is the probability that a volunteer is assigned an apron that is NOT green?
18/25
Mason plays a game by flipping two fair coins. He wins the game if both coins land facing heads up. If Mason plays 200 times, how many times should he expect to win?
1/2 of the time, 100 times
The spinner has eight equal-sized sections. The pointer lands on an even number 135 times out of 250 spins. Which of the following statements is true? Select all that apply:
Spinner: 1, 2, 3, 4, 5, 6, 7, 8
a) The pointer lands on an even number more often than expected.
b) The pointer lands on an even number less often than expected.
c) The expected probability of landing on an even number is 54%.
d) The actual probability of landing on an odd number is 46%.
e) It is equally likely that the pointer will land on an even or odd number.
a, d, e
Develop a probability model for rolling a cube with faces numbered 1-6.
Sample set- 1, 2, 3, 4, 5, 6
Probabilities:
1- 1/6
2- 1/6
3- 1/6
4- 1/6
5- 1/6
6- 1/6
Stacy uses a spinner with six equal sections numbered 2, 2, 3, 4, 5, and 6 to play a game. Which of the following statements is true? Select all that apply.
a) The probability of the pointer landing on an even-numbered section is 66.67%
b) It is impossible that the pointer will land on 1.
c) It is less likely that the pointer will land on an odd-numbered section.
d) It is certain that the pointer will land on a number less than 6.
e) The spinner is fair.
a, b, c
Mr. Sullivan places tiles numbered 1 through 18 in a bag and assigns a number to represent each of the 18 students in his class. Students will present their final reports in the order that their assigned tiles are drawn from the bag. Is Mr. Sullivan being fair? Why?
Yes; each has a 1/18 chance of being chosen.
Sanji throws an 8-sided solid with faces numbered 1 through 8. Which of the following statements is true? Select all that apply.
a) P(even number)=1/8
b) P(multiple of 3)=1/4
c) P(odd number)=1/2
d) P(number less than 8)=1
e) P(factor of 24)=3/4
f) P(the number 9)=0
b, c, e, f
Jessica records the number of winners at the Dunk-a-Teacher booth at the town fair as shown in the table. If there are 750 contestants on Monday, how many should Jessica expect to dunk a teacher?
Day Contestants Winners
Fri 215 27
Sat 417 54
Sun 368 39
90
Yasmin has a bag containing 165 colored beads. Her classmates take turns selecting one bead from the bag without looking, recording the color in the table, and replacing the bead. What is the experimental probability that a red bead is selected?
Color Red Brown Orange Yellow
#beads 10 15 17 13
10/55 = 2/11
Stacy uses a spinner with six equal sections numbered 2, 2, 3, 4, 5, and 6 to play a game. Stacy spins the pointer 120 times and records the results. The pointer lands 30 times on a section numbered 2, 19 times on 3, 25 times on 4, 29 times on 5, and 17 times on 6. How does the theoretical probability compare with the experimental probability of landing on an even number?
Theoretical- 4/6 = 66.67%
Experimental- 72/120 = 60%
It happened less than expected.
Miguel is comparing the probabilities of two spinners. Which of the following statements is true? Select all that apply:
Spinner A: 8 sections; 1, 2, 3, 4, 1, 2, 1, 2
Spinner B: 4 Sections; 1, 2, 3, 4
a) It is twice as likely that pointer A will land on 1 as compared to pointer B.
b) The probability that pointer B will land on an even number is 1/2.
c) The probability that pointer A will land on 1 is 3/8.
d) Spinner A is a fair spinner.
e) It is equally likely that pointer A will land on an odd number as compared to pointer B.
b, c, e
Two number cubes are rolled at the same time and the product is found (multiply the two numbers). What is the theoretical probability of rolling a product greater than 10?
All possible products:
1 2 3 4 5 6
1 1 2 3 4 5 6
2 2 4 6 8 10 12
3 3 6 9 12 15 18
4 4 8 12 16 20 24
5 5 10 15 20 25 30
6 6 12 18 24 30 36
17/36
A fair coin is flipped 10 times and lands on heads 8 times. Provide one reason to justify the difference between the experimental and theoretical probabilities.
The real world is never perfect; experimental probability will rarely match theoretical probability.
Yasmin has a bag containing 165 colored beads. Based on the table, about how many beads of each color are in Yasmin's bag?
Color Red Brown Orange Yellow
#beads 10 15 17 13
Red- 30
Brown- 45
Orange- 51
Yellow- 39
Does the following list represent a complete probability model?
P(red)=1/6
P(yellow)=1/3
P(blue)=1/12
P(green)=1/2
No
Holly throws a 12-sided number solid with faces labeled 1 through 12. What is the probability that Holly will roll a number greater than 12?
0/12, 0, impossible
Two number cubes are rolled at the same time and the product is found (multiply the two numbers).
If Abby rolls the number cubes 100 times, about how many times would she expect a product greater than 10?
All possible products:
1 2 3 4 5 6
1 1 2 3 4 5 6
2 2 4 6 8 10 12
3 3 6 9 12 15 18
4 4 8 12 16 20 24
5 5 10 15 20 25 30
6 6 12 18 24 30 36
about 47 times
In a bag of 25 marbles, 5 are red, 7 are blue, 10 are green, and 3 are yellow. The results of a marble being randomly selected and replaced 50 times are shown in the table. For which color is the experimental probability closest to the theoretical probability of being selected?
Color Frequency
Red 18
Blue 10
Green 15
Yellow 7
Yellow
The results of a survey asking 500 people about their favorite ice cream flavor are shown in the table. Find the experimental probability of each outcome in the sample space represented as a PERCENT.
Flavor # of people
Chocolate 90
Vanilla 125
Strawberry 60
Mint Chip 50
Other 175
Chocolate- 18%
Vanilla- 25%
Strawberry- 12%
Mint Chip- 10%
Other- 35%
Rachel plays a game by rolling two number cubes with sides numbered 1 through 6. To win the game, the sum of the numbers facing up must be 11. What is the probability that Rachel will win the game?
Table of Possible Sums:
1 2 3 4 5 6
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12
2/36 = 1/18 = 5.56%