Theoretical Probability
June rolls a six-sided number cube labeled 1 to 6. What is the probability of rolling an odd number?
3/6 or 0.5
Hasaan has a spinner with 5 equal sections, each a different color. After only 10 spins, the pointer had landed on red 40% of the time. After a whopping 1,000 spins, the pointer landed on red only 22% of the time. How can Hasaan account for this change in experimental probability?
As the number of trials increase, the experimental probability reaches closer to the theoretical probability. (The Law of Large Numbers)
Billy is attending an event where prizes are given away. The probability of winning movie tickets is 0.75 and the probability of winning a new TV is 0.04. How likely is it that Billy will win movie tickets or a new TV?
It is likely that Billy will win movie tickets, but very unlikely that he will win a new TV.
The number of runs that two baseball teams scored are shown below:
Team 1: 2, 3, 4, 1, 5, 6, 3
Team 2: 3, 4, 7, 10, 4, 3, 5
What is the mean absolute deviation for the team with the greatest variation in runs?
The mean absolute deviation of Team 2 is 1.9
Aimee is creating a spinner with 10 equal sections labeled A-I. How could Aimee have labeled her spinner if the probability of spinning a G is 2/10?
Aimee could label her spinner as follows:
A, B, C, D, E, F, G, G, H, I
Mark rolls a number cube 12 times, how many times would she expect a number greater than 4 to be rolled?
4 times
Jackson High School's Soccer team won 12, lost 5 and tied 3 of their first 20 games this season. Which outcome is most likely for the team's next game? (Explain your reasoning)
The team will most likely win as they have won 60% of their games this season.
How likely is it that that a coin that is flipped will land on heads?
As likely as not, or equally likely
The number of runs that two baseball teams scored are shown below:
Team 1: 2, 3, 4, 1, 5, 6, 3
Team 2: 3, 4, 7, 6, 4, 1, 5
Find the mean, median, mode and range of both teams. Which team on average scored more points?
Team 1: mean - 3.43, median - 3, mode - 3, range - 5
Team 2: mean - 4.29, median - 4, mode - 4, range - 6
Team 2 scored more points on average.
Anibelle has a box containing pencils and erasers. She told Cindy that the probability of randomly selecting an eraser is 1/5. Which of the following can be the content of the box?
a) 3 pencils and 1 eraser
b) 10 pencils and 2 erasers
c) 12 pencils and 4 erasers
d) 8 pencils and 2 erasers
A spinner has 8 equal-sided sections. To win the game, the spinner must land on a yellow section. If there are two yellow sections, what is the probability of a win.
2/8, 1/4, or 25%
A letter tile is randomly selected from a bag, recorded, and replaced 100 times. The results are listed below. What is the experimental probability of selecting the letter "E"? A = 16 E = 11 I = 29 O = 19 U = 25
11/100 or 0.11, or 11%
How likely is it that Archie randomly pulls a red marble out of a box with 2 red marbles, 3 blue marbles, and 1 yellow marble?
The chart below shows the number of hits in 5 games of two players.
Hits in 5 games
game #: 1 2 3 4 5
Kenny - 2 1 2 1 3
Peter - 0 3 1 2 2
Compare the mean and median of each player to determine who is the better hitter.
When looking at the mean, Kenny's mean is 1.8 hits per game and Peter's mean is 1.6 hits per game.
Kenny's median is 2
Peter's median is 2
The mean should be used to compare the two players, Kenny has a higher batting average by 0.2. Therefore, according to this data, Kenny is the better hitter.
Arnold wants to estimate the number of 6th grade students who like to play chess. He needs to create a random sample. How should Arnold collect his sample?
Arnold should ask 40, 6th grade students.
There are 3 red marbles, 2 green marbles, and 1 yellow marble in a box. What is the probability of pulling a red marble from the box?
3/6, or 0.50, 50%
Pedro recorded the types of birds that visit his bird feeder. Based on the results below, what is the probability the next bird will be a chickadee? Woodpecker = 3 Chickadee = 5 Cardinal = 1 Sparrow = 13 Blue Jay = 3
1/5, or 0.20, or 20%
If the probability of an event happening is 1, how likely is the event to happen?
It is certain that the event will happen.
Find the 5 number summaries of the ages of two fifth grade classes below, and create two box plots.
Class 1: 10, 10, 11, 11, 10, 12, 10, 10, 11, 11
Class 2: 10, 11, 11, 11, 12, 10, 10, 9, 11, 10
You will need to find the Upper Extreme, Lower Extreme, Median, Upper Quartile, and Lower Quartile of each data set. Then, compare the ages the students in class 1 and class 2.
Both classes have a median of 10.5 and an upper extreme of 12. The IQR of both classes is 1 year. 75% of the students class 1 are between 10 and 11 years old. 50% of the students in class 2 are between 10 and 11 years old.
John was conducting a survey to determine the favorite ice cream flavor of the students in his school. John asked his 5th grade math class to complete the survey.
Is this survey bias or not?
This survey is bias, John should have randomly selected students to survey in all grade levels.
A spinner with the numbers 1,2,3,4,5,6,7,8,9 is spun once. What is the probability of choosing an even number greater than 4?
A six-sided die is thrown 50 times. Using the list below, how does the theoretical probability of rolling a 3 compare to the experimental probability of rolling a 3? Number on Die How Many Times it Landed on that Number 1; 8 times, 2; 6 times, 3; 7 times, 4; 12 times, 5; 10 times, 6; 7 times.
The theoretical probability is higher than the experimental probability. (Theoretical = 17%, Experimental = 14%)
A fair spinner has the following numbers 1, 1, 1, 2, 2, 2.
How likely is it that a 3 will be spun?
Never going to happen.
Which of the two 5th grade classes ages has a Mean Absolute Deviation of 0.7 years?
Class 1: 10, 10, 11, 11, 10, 12, 10, 10, 11, 11
Class 2: 10, 11, 11, 11, 12, 10, 10, 9, 11, 10
Class 2 has a mean absolute deviation of 0.7 years.
A representative sample of 50 students were surveyed about what flavor ice cream they perferred. The table below shows their response:
Ice Cream Flavor Number of students
Vanilla 12
Chocolate 20
Strawberry 11
Mint Chocolate Chip 7
In a group of 300 students, how many students are expected to perfer chocolate ice cream?
120 students