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Pick
Me
Basic Probability
Population – a set of entities concerning
which statistical inferences are to be
drawn
 Random Sample – all member of
population and all group members of a
given size have equal chance of being in
the sample
 Sample Space- possible outcomes of an
experiment

Basic Probability
Experiment – any process that generates
one or more observable outcomes
(Drawing a card)
 Event – Any outcome or set of outcomes
in a sample (Drawing a king or queen)
 Probability Distribution – the probabilities
of an event occurring in the sample space

In your groups…

Given a bag of 100 marbles contains 50
red, 30 blue, 10 yellow, and 10 green find
the sample space, the probability
distribution, and the probability a blue or
green marble is drawn.

What in this problem is the event and
what is the experiment?
Mutually Exclusive vs.
Independent Events



Mutually Exclusive Events- two events or experiments which have
no outcomes in common P(A or B) = P(A) + P(B)
Independent Events- occurrence or non occurrence of one event
has no effect on probability of the other event (flipping a coin) P(A
and B) = P(A) x P(B)
Complement- set of all outcomes not contained in the event 1 - P
A pair of dice is rolled. The events of rolling a 6 and of rolling a double have the
outcome (3,3) in common. These two events are NOT mutually exclusive.
A pair of dice is rolled. The events of rolling a 9 and of rolling a double have NO
outcomes in common. These two events ARE mutually exclusive.
Some other examples of independent events are:
Landing on heads after tossing a coin AND rolling a 5 on a single 6-sided die.
Choosing a marble from a jar AND landing on heads after tossing a coin.
Choosing a 3 from a deck of cards, replacing it, AND then choosing an ace as the
second card.
Rolling a 4 on a single 6-sided die, AND then rolling a 1 on a second roll of the die.
In your groups…
Years of
Service
Number of
Employees
The chart on the right shows the data of a
company with employees who have been with
them for various periods of time.
0-4
157
5-9
89
If an employee is chosen at random, what is the
probability that the employee has 4 or fewer
years of service and 5 – 9 years of service?
10-14
74
15-19
63
Is this a mutually exclusive event or
independent?
20-24
42
25-29
38
30-34
37
35-39
21
40-44
8
In your groups…

The probability of winning a game is .1 or
10% suppose the game is played on two
different occasions.

What is the probability of winning both
games? Losing both games? And winning
once and losing once?
Random Variables


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Random Variable- a function that assigns a number to
each outcome in the sample space
The expected value is the sum of all the numerical
values times their respective probabilities.
Example: Outcome 15 16 17 18 19 20
Probability 0.1 0.3 0.2 0.2 0.1 0.1
Expected Value = 15(.1) + 16(.3) + 17(.2) + 18(.2) + 19(.1) + 20(.1) = 17.2
In your groups…



Calculate the probabilities of the sum of rolling two
dice? Example: Rolling snake eyes has a probability of
1/36.
What is the expected value of the experiment?
The sample space for rolling two dice is as follows:
Probability Density Functions
Probability
0.6
0.4
Probability
0.2
0
Red
Blue Yellow Green
Probability Density Function- any graph which corresponds to a
probability distribution
For example the above graph is of our data from the marble problem.
The area of each bar represents the probability of drawing that color
marble. The sum of all the areas equals 1.
Exit Problem…
Given a $1 lottery ticket with distribution
of winning :
$0 = .882746
$3 = .06
$5 = .04
$20 = .005
$40 = .002 $100 =.0002
$400 = .00005
$2500 = .000004
What is the expected value of the lottery
ticket and how much do you lose per play?
HINT:: Loss per play would equal the price
of the ticket minus the expected value.
Homework

Pgs 872-873

#9-10 (Independent Probability)

#18 and # 20 (Expected Value)

#23-26 (Probability Distribution,
Expected Value, Density Function)