Fundamentals of Probability 11'4

1
Fundamentals of Probability 11.4
Probability An event that is expressed as a
number.
Probabilities range from 0 to 1. 0 denotes an
event that cannot occur. 1 denotes an event that
is certain to occur.
Theoretical Probability applies to situations in
which the sample space only contains equally
likely outcomes.
2
Theoretical Probability of an event can be
calculated by dividing the number of outcomes
resulting in the event by the total number of
outcomes in the sample space.
Number of outcomes in event E
P( E )
Total number of possible outcomes
P( E )
3
Express the probability of each event as a
fraction in lowest terms.
Rolling a 4 on a die.
Sample Space
1, 2, 3, 4, 5, 6
Event
4
P( 4 )
4
Express the probability of each event as a
fraction in lowest terms.
Rolling a number greater than 2 on a die.
Sample Space
1, 2, 3, 4, 5, 6
Event
3, 4, 5, 6
P( gt 2 )
5
Express the probability of each event as a
fraction in lowest terms.
Rolling a number greater than 8 on a die.
Sample Space
1, 2, 3, 4, 5, 6
Event
0
P( gt 8 )
6
Express the probability of each event as a
fraction in lowest terms.
Being dealt a queen.
Sample Space
A,2,3,4 x 4
Event
Q x 4
P( Q )
7
Express the probability of each event as a
fraction in lowest terms.
Being dealt a card greater than 3 and less than
7.
Sample Space
A,2,3,4 x 4
Event
4, 5, 6 x 4
P( 3 lt c lt 7 )
8
Express the probability of each event as a
fraction in lowest terms.
Flipping a fair coin twice and getting two
tails.
Sample Space
H H, H T, T H, T T
Event
T T
P( T T )
9
Express the probability of each event as a
fraction in lowest terms.
Flipping a fair coin twice and getting at least
one head.
Sample Space
H H, H T, T H, T T
Event
H H, H T, T H
P( one H )
10
Express the probability of each event as a
fraction in lowest terms.
After selecting all the families with three
children, what is the probability of finding one
in which the family has exactly one male child.
Sample Space
MMM, FFF,
Event
MMM, MMF, MFF,
P( one M )
11
Express the probability of each event as a
fraction in lowest terms.
After selecting all the families with three
children, what is the probability of finding one
in which the family has at least two female
children.
Sample Space
MMM, FFF,
Event
M F F, F M F, F F M, F F F
P( at least 2 F )
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Homework

• Pg 585
• 3 48 multi of 3