Theoretical Probability
Experimental Probability
Tree Diagrams
Organized List
Make it a percent
100
What is Theoretical probability ?
Theoretical probability is a probability that is expected
100
What is Experimental probability? Are the outcomes typically the same as Theoretical Probability
Experimental probability is the actual result of an experiment, which may be different from the theoretical probability
100
What is a tree diagram and what is it used for?
Tree diagrams are a helpful tool to help you visualize probability and all possible outcomes for an event
100
What is an organized list in math?
A table or chart used to organize data from a math problem, and to help you to discover relationships and patterns amongst data!
100
How do you convert a fraction into a percent?
First divide the numerator by the denominator, and then multiply the decimal by 100 .
200
What is the formula to calculate Theoretical probaility?
200
What is the formula used to to calculate Experimental probability?
Experimental probability =
# of favourable outcome
_____________________
# of total trials
200
Bianca and Olivia are each picking candy canes out of two separate boxes. What is the FIRST THING we need to do when creating a tree diagram?
Add our headings/labels
Ex: Box 1, Box 2, Outcomes
200
When you are beginning your organized list, what must we ensure we are starting with?
As you write your list, start with your largest denomination at the top! (Largest denomination = biggest number, highest value etc.)
200
Erik, Liz, and Anne are playing a game. Their probabilities of winning the game are as follows:
P(Erik wins) = 0.4
P(Liz wins) = 1/2
P(Anne wins) = 0.06
Convert each players P(of winning) into a percent.
Who is most likely to win?
P(Erik wins) = 40%
P(Liz wins) = 50%
P(Anne wins) = 6%
Liz is most likely to win.
300
A bag contains 10 red marbles, 8 blue marbles and 2 yellow marbles. Find the theoretical probability of P(blue marble)
P(blue marble) = 8/20
= 2/5
300
The winter clothing drive has received donations of 15 coats, 30 pairs of gloves, 18 scarves, and 25 hats so far. What is the Experimental P(NOT gloves)?
P(NOT gloves) = 58/88
= 29/44
300
A bag contains 3 black balls and 3 white balls, a second bag contains 2 black balls and 1 white ball. Paul picks a ball from bag 1 and then picks another ball at random from bag 2.
a) Create a probability tree to display all possible outcomes
b) What is P(2 black balls)
c) P(picking a black ball second)
b) P(2 black balls)= 4/15
c) P(picking a black ball second)= 10/15
= 2/3
300
Debbie put 25 cents in a vending machine. The vending machine glitches and spits out Debbies change in small coins. Use an organized list to display the coin combinations that the vending machine could give Debbie back.
How many possible combinations are there? What are they?
3.
- 2 dimes, 1 nickel
- 1 dime, 3 nickels
- 5 nickels
300
Professor Oat, Horsey Long Legs, and Thunderbolt are race horses. Their probabilities of winning the race are as follows:
P(prof.oat winning) = 3/10
P(h.long legs winning) = 0.6
P(thunderbolt winning) = 18/24
Convert each race horses P(of winning) into a percent.
Who is most likely to win?
P(prof.oat winning) = 30%
P(h.long legs winning) = 60%
P(thunderbolt winning) = 75%
Thunderbolt is most likely to win.
400
The spinner below has 6 equal sectors coloured red, purple, blue, yellow, orange and green. What is the theoretical P(green)?
f P(green) = 1/6
400
The following table displays the number of children that members of a fitness club have. Based on this data, what is the Experimental P(fewer than 3 children)
Number of children|Number of members
_________________________________
1 | 6
2 | 4
3 | 8
4 | 1
5 | 1
P(fewer than 3 children)= 10/20
= 1/2
400
Bag A contains 5 marbles of which 2 are red and 3 are black. Bag B contains 6 marbles of which 2 are red and 4 are black. A ball is drawn at random from each bag.
a) Draw a probability tree diagram to show all the outcomes the experiment.
b) P(both are red)
(c) P(both are black)
(d) P(one black and one red)
(e) P(at least one red)
b) P(both are red) =4/30
= 1/15
(c) P(both are black)= 12/30
= 2/5
(d) P(one black and one red)= 14/30
= 7/15
(e) P(at least one red)= 18/30
= 3/5
400
Ryan wants to purchase a can of iced tea for 75 cents. He has quarters, dimes and nickels in his backpack. Make an organized list to display all possible coin combinations Ryan can use to pay for his drink.
How many combinations require him to pay with more than 5 coins
9 coin combinations will have Ryan paying with more than 5 coins
400
The probability of it snowing in Eastern Canada tomorrow is 0.4. The probability of it snowing in Western Canada tomorrow is 2/5. Convert each probability into a percent. Which event is more likely?
Eastern Canada = 40% snow
Western Canada = 40% snow
It is equally likely that it will snow in both Eastern Canada and Western Canada.
500
Joel's Spotify playlist has 20 classical songs, 31 rock songs, and 14 rap songs on it. When he puts it on shuffle, what is the theoretical P(rock or rap song)?
P(rock or rap song) = 45/65
= 9/13
500
Pizza Nova made 79 cheese pizzas, 45 veggie pizzas, 63 pepperoni pizzas, and 21 sausage pizzas on Friday night. What is the Experimental P(next pizza will be meatless)? Share you answer in a percent
P(next pizza will be meatless)= 124/208
= 31/52
57% chance of the next pizza ordered being meatless.
500
A box contains 4 red and 2 blue chips. A chip is drawn at random and then replaced. A second chip is then drawn at random.
a) Show all the possible outcomes using a probability tree diagram.
b) P(at least one blue)
(c) P(one red and one blue)
(d) P(two of the same colour)
b) P(at least one blue)= 20/36
=5/9
(c) P(one red and one blue)=16/36
=4/9
(d) P(two of the same colour)=20/36
=5/9
500
Jamie bought 2 lollipops for $1. Make an organized list to display the coin combinations Jamie could have used to pay for her lollipops (no pennies).
What is the highest number of coins she could have used? (not highest value, # of coins)
20 nickels (20 x 5 cents = $1.00)
500
Pablo, Mateus, and Ling are competing in a burrito-eating contest. Their probabilities of winning the contest are as follows:
P(Pablo wins) = 3/9
P(Mateus wins) = 13/26
P(Ling wins) = 18/25
Convert each probability into a percent. Who is most likely to win?
P(Pablo wins) = 33%
P(Mateus wins) = 50%
P(Ling wins) = 72%
Ling is most likely to win.