probability theoretical theoretical probability can be found without doing and experiment....
TRANSCRIPT
Probability
Probability
THEORETICAL
Theoretical probability can be found without doing and experiment.
EXPERIMENTAL
Experimental probability is found by repeating an experiment and observing the outcomes.
• I am going to take 1 marble from the bag.• What is the probability that I will pick out
a red marble?
Theoretical Probability
I have three marbles in a bag.
1 marble is red
1 marble is blue
1 marble is green
Theoretical Probability• Since there are three
marbles and only one is red, I have a 1 in 3 chance of picking out a red marble.
• I can write this in three ways:
• As a fraction: 1/3• As a decimal: .33• As a percent: 33%
Experimental Probability
• Notice the Experimental Probability of drawing a red, blue or green marble.
Marble number red blue green
1 12 13 14 15 16 1
Total 2 1 3
Exp. Prob.
2/6 or 1/3 1/6
3/6 or 1/2
Simple Probability
The probability of one independent event.
An independent event is one that does not affect the outcome (or probability) of any other event.
Simple Probability
probability of an event or P(event)
isnumber of favorable outcomes
total number of possible outcomes
Simple Probability
probability of an event or P(event)
isnumber of favorable outcomes
total number of possible outcomes
Example 1:Sarah rolls two 6-sided numbered cubes. What is the probability that the two numbers added together will equal 5?
Simple Probability
probability of an event or P(event)
isnumber of favorable outcomes
total number of possible outcomes
Example 1:Sarah rolls two 6-sided numbered cubes. What is the probability that the two numbers added together will equal 5?
4/36 = 1/9
Simple Probability
probability of an event or P(event)
isnumber of favorable outcomes
total number of possible outcomes
Example 1:Sarah rolls two 6-sided numbered cubes. What is the probability that the two numbers added together will equal 5?
4/36 = 1/9
Simple Probability
Example 2:What is the probability of drawing a king from a deck of cards?
probability of an event or P(event)
isnumber of favorable outcomes
total number of possible outcomes
Example 1:Sarah rolls two 6-sided numbered cubes. What is the probability that the two numbers added together will equal 5?
4/36 = 1/9
Simple Probability
Example 2:What is the probability of drawing a king from a deck of cards? 4/52 or 1/13
probability of an event or P(event)
isnumber of favorable outcomes
total number of possible outcomes
Example 1:Sarah rolls two 6-sided numbered cubes. What is the probability that the two numbers added together will equal 5?
4/36 = 1/9
Simple Probability
Example 2:What is the probability of drawing a king from a deck of cards? 4/52 or 1/13
Example 3: What is the probability of drawing a queen of hearts from as deck of cards?
probability of an event or P(event)
isnumber of favorable outcomes
total number of possible outcomes
Example 1:Sarah rolls two 6-sided numbered cubes. What is the probability that the two numbers added together will equal 5?
4/36 = 1/9
Simple Probability
Example 2:What is the probability of drawing a king from a deck of cards? 4/52 or 1/13
Example 3: What is the probability of drawing a queen of hearts from as deck of cards?
1/52
Example 1:Sarah rolls two 6-sided numbered cubes. What is the probability that the two numbers added together will equal 5?
Simple Probability
Example 2:What is the probability of drawing a king from a deck of cards?
Example 3: What is the probability of drawing a queen of hearts from as deck of cards?
Compound Probability
• The probability of two independent events• If an event is independent, it does not affect
the outcome of other events.
“OR”
• P(A or B) = P(A) + P(B)Example: When you flip a fair coin and roll a
number cube, what is the P(head or 4)?
P(head or 4) = ½ + 1/6 = 3/6 + 1/6 = 4/6 = 2/3
• Example: Alfred is going to the Lakeshore Animal Shelter to pick a new pet. Today, the shelter has 8 dogs, 7 cats, and 5 rabbits available for adoption. If Alfred randomly picks an animal to adopt, what is the probability that the animal would be a cat or a dog?8/20 + 7/20
= 15/20 = 3/4
“And”
• P(A and B) = P(A) x P(B)• Example: When you flip a fair coin and roll a
number cube, what is the P(head and 4)?• P(head, 4) = ½ x 1/6
= 1/12
Practice
1. P(heads, hearts) = 13/104
2. P(tails, four) = 4/104