Unit 4

1
Unit 4 Combinatorics and ProbabilitySection
4.3 An Introduction to ProbabilityCalculator
Required
2
number of winners
compute second
Probability
compute first
Ratios reduce like fractions
3
Independent
Dependent
Consistent Denominator For each individual trial
Denominator Reduces For each individual trial
4
Find the probability that a four digit number
created from the digits 2, 4, 5, 8 is less than
4000. Assume repetition is not allowed.
A ball contains three red balls, two blue balls,
and one white ball. If two are drawn and
replacement is allowed, find the probability
that both are red.
5
Two die are rolled. Find the probability that
neither is a 5.
Independent vs. Dependent Events Rule of Thumb

• Do the event twice
• On the second time of event, check number of
  possibilities

If the same..independentseparate fractions
If differentdependent...single fraction.
most likely
combinations to be used
6
A single ball is drawn from a bag containing four
red, five white and two green balls. Find the
probability of each event. a. A red or
green ball is drawn
b. A white or red ball is drawn
7
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
b. Find the probability that the first pastel is
yellow and the second pastel is red.
8
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
9
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.
b. Ray and Paula ask him, but Leon does not
10
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
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)
12
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
13
State the odds of an event occurring given the
probability of the event.
14
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
ODDS
7922598168
33108257
15
From a standard deck of cards, five are drawn.
What are the odds of each selection?
b. five from one suit
ODDS
51482593812
2574129691
16
From a standard deck of cards, five are drawn.
What are the odds of each selection?
b. Two of one suit, three of another