Download Expressing Probability

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 Notes Lesson 2: Probability
Accel Precalculus
Unit 1: Probability and Statistics
Lesson 2: Probability
EQ: How do you find probability of mutually
exclusive events, independent events, and
complements of event?
p. 674
How do some businesses, such as life insurance
companies, and gambling establishments, make
dependable profits on events that seem
unpredictable?
Businesses have discovered that the overall
likelihood, or probability, of an event can
be discovered by observing the results of a
large number of repetitions of the
situation in which the event may occur.
 New Terminology:
DEFINITION
Trial: a systematic opportunity
for an event to occur
EXAMPLE
rolling a die
Experiment: one or more trials
rolling a die 10 times
Sample Space: the set of all
possible outcomes of an event
1, 2, 3, 4, 5, 6
Event: an individual outcome
or any specified combination
of outcomes
rolling a 3
rolling a 3 or rolling a 5
Outcomes are random if all possible outcomes are
equally likely.
Now Try p. 682 #1
In Exercises 1 – 6, determine the sample
space for the given experiment.
1. A coin and a six-sided die are tossed
S = {H1, T1, H2, T2, H3, T3, H4, T4, H5, T5, H6, T6}
 Expressing Probability:
1.
must be a number from 0 to 1, inclusive
2.
may be written as a fraction, decimal, or percent
3.
an impossible event has a probability of 0
4.
a certain event has a probability of 1
5.
the sum of the probabilities of all outcomes in a
sample space is 1
Now Try p. 682 #7
7 – 10,
7.
E = { HTT, THT, TTH}
3
P( E ) 
5
TOSSING A DIE In Exercises 15–18, find the probability
for the experiment of tossing a six-sided die twice.
15. The sum is 5.
E = { (1, 4),(2, 3), (3, 2), (4, 1)}
4 1
P( E ) 

36 4
**RECALL the FCP:
6  6  36 total outcomes
Now Try p. 682 #21
DRAWING MARBLES In Exercises 21–24, find the
probability for the experiment of drawing two
marbles(without replacement) from a bag containing
one green, two yellow, and three red marbles.
NOTE: No Replacement!
21. Both marbles are red.
Draw 2 red out of 3 red
Draw 2 red out of 6 total
6
C2  15
3
C2  3
C2 3 1
P(red & red ) 
 
15 5
6 C2
3
3 2 1
P(red & red )   
6 6 5
WHY?
Now Try p. 684 #49
***Combination because ORDER doesn’t matter
C4 14
a ) P (4 good ) 

15
12 C 4
9
9 8 7 6 14
P (4 good )     
12 11 10 9 15
C2 3 C2 12
b) P ( 2 good ) 

55
12 C 4
9
C3 3 C1 28
c ) P (3 good ) 

55
12 C 4
9
14 28 12 54
P (3 good ) 



55 55 55 55
Now Try p. 682 #52
52.
1 1 1
a ) P(even, even)   
2 2 4
1 1 1 1 1 1 1
b) P(even odd or odd even)       
2 2 2 2 4 4 2
29 29 841
c) P(#  30 , #  30 ) 


30 30 1600
40 1
1
d ) P ( same # , same # ) 


40 40 40
Now Try p. 682 #54
P(available) = 0.9
P(not available) = 0.1
a ) P (both avail )  0.9   0.81
2
b) P (neither avail )  0.1  0.01
2
c) P(at least 1 avail )  1  P(neither )  1  0.01  0.99
ASSIGNMENT:
p. 682 – 685
#6, 10, 18, 23, 24, 41, 50, 51, 55