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5.1 Introducing Probability
Objectives:By the end of this section, I will beable to…
1) Understand the meaning of an experiment, an outcome, an event, and a sample space.
2) Describe the classical method of assigning probability.
3) Explain the Law of Large Numbers and the relative frequency method of assigning probability.
Rules of Probability
1. Probabilities must be between 0 and 1.
2. For any experiment, the sum of all outcome probabilities must = 1
Probability termsOutcome: result of experiment.
Sample Space: all the possible outcomes of experiment
PROBABILITY
𝑝 (𝐴)=number of favorable outcomessample space
𝑝 (𝐴)=number of favorable outcomesTOTAL number of outcomes
Experimental Probability vs. Theoretical Probability
Roll ONE die 15 times.
WRITE OUT your results.
What is your probability of rolling a FIVE?
This is an example of experimental probability.
ONE DIE
THEORETICAL PROBABILITY
1) What is the probability that
you will roll a 5?
5 = 1 ways__1
6
TWO DICETwo dice are rolled at the same time.
Find the sample space.
1,1
1,2
1,3
1,4
1,5
1,6
2,1
2,2
2,3
2,4
2,5
2,6
3,1
3,2
3,3
3,4
3,5
3,6
4,1
4,2
4,3
4,4
4,5
4,6
5,1
5,2
5,3
5,4
5,5
5,6
6,1
6,2
6,3
6,4
6,5
6,6
361,2
2,1
__
TWO DICE
4) With two dice, what is the probability that you will roll a seven?
5) With two dice, what is the probability that you will roll a number larger than 10?
= 6 ways1,6 5,22,56,1 4,3 3,4
6
365,6
6,511
6,6 = 3 ways __3
3612
DECK OF CARDS How many cards are in a deck? How many face cards are there? How many suits are in a deck of cards? How many cards are in each suit?
52
124
13
__
DECK OF CARDSWhat is the probability of getting…
A face card?
A red two?
12 = # of face cards
52 = sample space
2 = # of red twos
52 = sample space
Tree Diagrams
1
2
1
2
1
2
Toss a Coin
H
TH
T
H
T
P(H) = P(H) = 1/2
P(H,H) = P(H,H) = ½ · ½ = ¼
1
2
1
2
1
2
Use the following table to find the probability
Find the probability that a randomly selected worker at McDonalds2) Is a college grad3) Is a male4) Is a male who graduated from Grad school
HS College Graduate
MALES 20 27 31
FEMALES 26 36 29
27
36
63 169
63 / 169
20 31 7827
78 / 169
31
31 / 169
Scenarios
A slot machine in VEGAS has three wheels, and each wheel has a picture of a lemon, cherry, and an apple on it. Each wheel operates independently of the other. When all three wheels show the same item, then the player wins $5000. Find the probability of a player winning $5000
when playing this slot machine.
Forgetful Students
Sallies students are very forgetful. Three of Mrs. Godfrey’s seniors left their calculators in her classroom. They all stop by after school at different times and randomly select a calculator. The calculators all look exactly the same too! What is the probability that they pick the correct one?