Post on 01-Apr-2015
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Unit 4 – Combinatorics and ProbabilitySection 4.3 – An Introduction to Probability
Calculator Required
Probability = number of possibilities compute first
number of winners compute second
What
How
are
do you w
you do
?
?
in
ing
0 P E 1
P winning 1 P losing
number of winne number ofO dd lor ss s : ser
Ratios reduce like fractions
Independent DependentRoll a Die Twice
6 6Draw two cards with replacement
52 52
Draw two cards without replacement
52
2
Choose two lettersRepetition allowed
26 26
Choose two lettersRepetition NOT allowed
26
2
Consistent DenominatorFor each individual trial
Denominator ReducesFor each individual trial
Find the probability that a four digit number created from thedigits 2, 4, 5, 8 is less than 4000. Assume repetition is notallowed.
4 3 2 1 1 3 2 1
A ball contains three red balls, two blue balls, and one whiteball. If two are drawn and replacement is allowed, find the probability that both are red.
63
63
Two die are rolled. Find the probability that neither is a 5.
65 5
6
Independent vs. Dependent Events Rule of Thumb
-Do the event twice-On the second time of event, check number of possibilities
If the same…..independent…separate fractionsIf different……dependent…...single fraction…. most likely combinations to be used
4 2
1 1
11 11
1 1
6
11
b. A white or red ball is drawn
5 4
1 1
11 11
1 1
9
11
A single ball is drawn from a bag containing four red, five whiteand two green balls. Find the probability of each event. a. A red or green ball is drawn
In a box there are three red, two blue, and three yellow pastels. Doris randomly selects one, returns it, and then selects another.
a. Find the probability that the first pastel is blue and the second pastel is blue 2 2
1 1
8 8
1 1
1
16
b. Find the probability that the first pastel is yellow and the second pastel is red.
3 3
1 1
8 8
1 1
9
64
When Carlos shoots a basketball, the probability that he will make a basket is 0.4. When Brad shoots, the probability of a basket is 0.7. What is the probability that at least one basket is made if Carlos and Brad take one shot each?
P(at least one) = 1 – P(none)
P(at least one basket) = 1 – P(no baskets)
P(Carlos missing) = 0.6 P(Brad missing) = 0.3
1 0.6 0.3
0.82
The probability that Leon will ask Frank to be his tennis partner is ¼, that Paula will ask Frank is 1/3 and that Ray will ask Frank is ¾. Find the probability of each event. a. Paula and Leon ask him.
1 1 1
3 4 12
b. Ray and Paula ask him, but Leon does not
33
4
1 3
4 3 16
The probability that Leon will ask Frank to be his tennis partner is ¼, that Paula will ask Frank is 1/3 and that Ray will ask Frank is ¾. Find the probability of each event. c. At least two of the three ask him.
Leon Yes Paula Yes Ray No
Leon Yes Paula No Ray Yes
Leon No Paula Yes Ray Yes
Leon Yes Paula Yes Ray Yes
11
4
1 1
4 3 48
2
3
1 3 1
4 4 8
1 3 3
3 4 1
3
4 6
1 1 3 1
4 3 4 16
1 1 3 1 19
48 8 16 16 48
The probability that Leon will ask Frank to be his tennis partner is ¼, that Paula will ask Frank is 1/3 and that Ray will ask Frank is ¾. Find the probability of each event.
d. At least one of the three ask him.
P(at least one) = 1 – P(none)
P(at least one will ask) = 1 – P(none ask)
3 2 1
4 3 4
71
8
According to the weather reports, the probability of snow on a certain day is 0.7 in Frankfort and 0.5 in Champaign. Find the probability of each:
7 5 7
10 10 20
7 5 7
10 10 20
3 5 3
10 10 20
a. It will snow in Frankfort, but not in Champaign.
b. It will snow in both cities.
c. It will snow in neither city.
d. It will snow in at least one of the cities.
3 5 171
10 10 20
State the odds of an event occurring given the probability ofthe event.
4a.
9 4
P W9
4 5P L 1
9 9 4 5
ODDS : 4 : 59 9
1b.
12 1
P W12
1 11P L 1
12 12 1 11
ODDS : 1:1112 12
From a standard deck of cards, five are drawn. What are the odds of each selection?
a. five aces
Zero…..there are only four aces in a deck.
b. five face cards
12 40
5 0P W
52
5
12 40
5 0P L 1
52
5
792P W
2598960 2598168
P L2598960
ODDS
792:2598168
33:108257
From a standard deck of cards, five are drawn. What are the odds of each selection?
b. five from one suit
134
5P W
52
5
134
5P L 1
52
5
5148P W
2598960 2593812
P L2598960
ODDS
5148:2593812
2574:129691
From a standard deck of cards, five are drawn. What are the odds of each selection?
b. Two of one suit, three of another
13 1312
3 2P W
52
5
13 1312
3 2P L 1
52
5