Calculate Theoretical Probability
Maria is flipping a standard quarter with heads on one side and tails on the other. What is the theoretical probability the coin will land on heads?
1/2 or 0.5 or 50%
There are two possible outcomes. Flipping heads and flipping tails. The number of favorable outcomes (1 representing heads) is placed over the total number of outcomes (2).
Mr. Ruxton flips a quarter 100 times. The quarter lands on heads 55 times. What is the experimental probability of landing on heads?
11/50
You place the number of times the event (head, 55) over the total number of trials (100).
55/100 --> 11/50
Theoretical probability is calculated BEFORE an event occurs and does not change.
True
Define "theoretical probability."
It is the probability of what you expect to occur.
What is the sample space of selecting a marble from a bag that contains 3 red marbles, 2 blue marbles, and 4 green marbles?
S = (R, R, R, B, B, G, G, G, G)
There is a jar with 20 marbles of varying color. 7 are green, 4 are blue, and 9 are red. What is the theoretical probability of selecting a blue marble?
1/5 or 0.2 or 20%
The number of favorable outcomes (4 representing blue marbles) is placed over the total number of outcomes (20).
4/20 --> 1/5
A six sided, standard die with numbers 1-6 is rolled 30 times. The results are shown below.
1 = 5 times 2 = 7 times 3 = 4 times 4 = 8 times 5 = 3 times 6 = 3 times
What is the experimental probability of rolling a 6?
1/10
You place the number of times the event occurred (6, 3 times) over the total number of events 30.
3/30 --> 1/10
Experimental probability is known as relative frequency?
True
Define "experimental probability."
The probability of what actually occurs.
What are the two major components of a probability model?
Sample space and list of the probabilities of all the possible outcomes.
A random number is selected between 1 and 50. What is the theoretical probability the number selected is a multiple of 9?
1/10 or .10 or 10%
There are 5 multiples of 9 between 1 and 50. They are 9, 18, 27, 36, and 45.
5/50 --> 1/10
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%
The number of times the event ("E") occurred (11 times) is placed over the total number of trial (100)
Green = 4 times Blue = 4 times Red = 2 times
The theoretical probability of selecting a blue marble is 4/10 which is 2/5 when reduced.
False
The theoretical probability is based on what you expect not on results. There are 3 blue marbles so the theoretical probability is 3/10.
What is the definition of relative frequency?
The relative frequency is the ratio of the number of times an event occurs to the total number of trials.
List all the probabilities of all possible outcomes of a spinner that has 3 red spaces, 2 green spaces, 1 black space, and 6 blue spaces.
p (r) = 1/4
p (g) = 1/6
P (blk) = 1/12
p (blu) = 1/2
You just got TikTok on your phone and you immediately start following 3 of your friends who have all posted videos today. The first friend posted 4 videos, the second friend posted 7 videos, and the third friend posted 11 videos. Using theoretical probability, how many videos would you expect your first friend to have posted if there were 88 videos?
16 videos.
The first friend posted 2/11 videos on the first day (Reduce!). Using proportional reasoning we can set up the equation 2/11 = v/88. V represents what were trying to find out.
v = 16
Pedro recorded the types of birds that visit his bird feeder. Based on the results below, what is the experimental 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%
The number of times the event occurred (chickadee, 5) is placed over the total number of trials (25).
5/25 --> 1/5
As you increase the number of trials you should expect your experimental probability to move closer to your theoretical probability.
True (Law of Averages, Law of Large Numbers)
Define outcome and event.
Outcome is the possible results of an action.
An event is a set of outcomes.
Develop a probability model of rolling a 6 sided standard die with numbers 1-6.
S = (1, 2, 3, 4, 5, 6)
P(1) = 1/6 P(2) = 1/6 P(3) = 1/6 P(4) = 1/6 P(5) = 1/6 P(6) = 1/6
Jarvonya spins a spinner with 5 equal sections numbered 1-5 and she spins another spinner with 5 equal sections with the letters A-E. What is the probability she will spin a 4 and a B?
1/25 or 0.04, or 4%
The total number of favorable outcomes (1 representing 4-B) is placed over the total number of outcomes (25)
***Bonus Points*** For an additional 500 points can you list all 25 of the possible outcomes?
A bag contains different coins. Mr. Ruxton randomly selected a coin, recorded the results, and replaced the coin. He did this several times. Below are the results
Pennies = 4 times Nickels = 5 times Dimes = 8 times Quarters = 7 times
What is the experimental probability of selecting a quarter?
7/24
You place the number of times the event occurred (quarter, 7 times) over the total number of trials (24)
A sample space is a list of all the probabilities of an event.
False. A sample space is a list of all the possible outcomes.
When you combine the sample space with a list of all the probabilities of an event you now have what's called a probability model.
Probability is measured how? What are the three types of numerical values we use to show probability?
Probability is measured using numbers between 0 and 1 (fractions, decimals, and percent)
Develop a probability model for flipping a quarter twice.
S = (HH, TT, HT, TH)
P(HH) = 1/4 P(TT) = 1/4 P(HT) = 1/4 P(TH) = 1/4
Bonus Points (100): Why are there two different outcomes when the result is one heads and one tails?