Theoretical
Experimental
Simulations
Compound Events
Random
100
What is theoretical probability?
The expected probability of an event
100
Jake 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 Jake account for this change in experimental probability?
As the number of trials increase, the experimental probability reaches closer to the theoretical probability.
100
Darian made 8 of the 12 free throws he attempted. He wants to simulate how many free throws he will make in the next 22 games. Darian makes a spinner with 3 equal sections, where 2 represent the shots made and 1 represents the shots missed. Explain why this will or will not work.
This will work because 8/12 times he makes it, which simplifies to 2/3. So, 2 of the sections represent the shots he makes, and 1 represents the shot he missed. He will spin it 22 times.
100
You flip a coin and then roll a fair six-sided die. What is the probability the coin lands heads up and the die shows a one?
1/12
100
How many outfits can be created from 5 pairs of jeans, 10 shirts and 3 pairs of sneakers?
150 outfits
200
A bag of marbles has 3 red marbles, 5 black marbles, and 2 white marbles. What is the probability of pulling out a red marble?
3/10 or 30%
200
What is experimental probability?
The test with results, showing varying outcomes. What actually happens in an experiment- the real results.
200
Judy did not study for her math test. It has 10 True-False questions. She makes a spinner with 10 equal sections, with 1 labeled "T" and the 1 labeled "F". She leaves the other sections blank. Explain whether this simulation works or does not work.
This simulation does not work because she has a 50/50 chance of getting the question right. So, she could flip a coin 10 times, etc.
200
Four coins are tossed. What is the probability that all four coins land on heads?
1/16
200
There are 70 marbles in a bag.
15 are blue, 30 are red, 20 are orange and 5 are yellow.
What is the probability you would not pick an orange marble in simplest form?
5/7
300
I have a pack of Starburst. There are 38 orange, 13 red, and 25 yellow. What is the probability that I pick an orange one?
38/76=1/2=50%
300
How many different license plates can be made with the following characteristics if letters and numbers CAN be repeated?
a) 3 letters and 3 numbers
b) 2 letters and 4 numbers
A.) 26x26x26 (letters) x 10x10x10
17576000
B.) 26x26x10x10x10x10
6,760,000
300
In planning for her birthday, Kelly is trying to predict which kind of ice cream each of her 10 friends will choose. Her friends can choose from chocolate, vanilla, strawberry, or cookies-n-cream ice creams. Which of the following could Kelly use to make her prediction of which kind of ice cream her 10 friends will choose? Select all that apply.
a) Roll a six-sided die 10 times.
b) Flip four coins 10 times.
c) Spin a spinner with four equal different colored sections 10 times.
d) Draw either a heart, a diamond, a spade or a club from a deck of cards 10 times, with replacement.
C or D
300
A card is chosen at random from a deck of 52 cards. It is replaced and a second card is chosen. What is the probability you draw an 8, then a jack?
4/52x 4/52
1/13 x 1/13
1/169
300
James had to choose between yellow, purple, green, blue, or orange wallpaper and orange, blue, red, green, or yellow carpet. Find the total number of possible outcomes when he selects one color of wallpaper and one color of carpet.
25
400
There are 70 marbles in a bag.
15 are blue, 30 are red, 20 are orange and 5 are yellow.
What is the probability you would pick a blue marble in simplest form?
3/14
400
Mr. Holm spun a spinner 150 times. His results are recorded below.
Green: 25
Yellow: 60
Orange: 15
Pink: 50
What was the experimental probability of spinning Orange?
15/150=1/10=0.1=10%
400
Drought is shown by 10% or number 1.
2/10 or 20%
400
A jar holds 15 red pencils and 10 blue pencils. One pencil is chosen, replaced, then a second pencil is chosen. What is the probability of choosing a red pencil, then another red pencil.
9/25
or 36%
400
I flipped a coin 75 times. I got heads 40 times and tails 35 times.
Compare the experimental probability of landing on heads to the theoretical probability of landing on heads.
Experimental: 40/75=8/15=0.53=53%
Theoretical: 1/2=0.5=50%
The experimental probability is greater than the theoretical probability
500
Terry rolls a number cube and records an even number 9 times in a row. As the number of times she rolls an even number increases, what happens to the theoretical probability that she rolls an even number?
The probability is 50%
500
The probability that a student walking into your school is in seventh grade is 40%. The probability that a student walking into your school is a girl is 60%. Design a simulation to estimate the experimental probability that the next student to walk into your school is a seventh grade girl.
Answers vary due to data.
Theoretical is 24%
500
Based on the data, what is the experimental probability that exactly four contestants to get a winner in the 10 trials?
10%
** In Trial 6 this shows on the fourth contestant they won, so 1 out of 10 trials
500
How many different license plates can be made with the following characteristics if letters and numbers CAN be repeated?
a) 3 letters and 3 numbers
b) 2 letters and 4 numbers
a.) 26x26x26x10x10x10
175,760,000
b.) 26x26x10x10x10x10
6,760,000
500
A toy vending machine contains football helmets and sticky hands. There are 36 items in the machine. Winning a football helmet has five times as many favorable outcomes as winning sticky hands. How many of each item is in the machine?
Helmet: 30
Sticky hands: 6