Announcements
Finite Probability
Monday, October 17th
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MyMathLab 5 is due tonight!
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Problem Set 5 is due Wednesday Oct 19
Today: Sec. 6.5: Tree Diagrams
Organize conditional probabilities with a tree diagram
Solve probability questions by “walking down branches”
of a tree diagram
Next Class: Sec. 6.5: Tree Diagrams II
Cherveny
Oct 17
Math 1004: Probability
Warm-up: Kittens
Example
Suppose that there is an orange room containing two kittens with
orange collars and one kitten wearing a black collar and there is a
black room containing one kitten wearing a black collar and three
kittens wearing orange collars. An experiment consists of selecting
a kitten at random from the black room and then (you keep the
first kitten) selecting at random a kitten from the room having the
color collar your kitten is wearing. Find the probability that the
second kitten is wearing a orange collar.
Answer: P(2nd kitten orange collar) =
Cherveny
Oct 17
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Math 1004: Probability
Tree Diagrams
Definition
A tree diagram organizes the outcomes in an experiment as
branches of a tree. Each branch is labeled with the probability of
taking that outcome, given the previous branches.
Key Idea: The probability of a particular sequence of outcomes is
given by multiplying the probabilities found on those branches of
the tree.
Cherveny
Oct 17
Math 1004: Probability
Computer Diagnostic
Example
Apple uses a two-step diagnostic procedure to repair computers.
Step I locates the problem in a computer with probability 0.8. Step
II (which is executed only if step I fails to locate the problem)
locates the problem with probability 0.6.
What is the probability that the procedure will fail to locate the
problem?
P(Fail to detect) = (.2)(.4) = .08
Cherveny
Oct 17
Math 1004: Probability
Cards
A card is drawn from a 52-card deck. If the card is a face card
(Jack, Queen, King), we toss a coin. If not a face card, roll a die.
(a) Find the probability that we end with a “6” on the die.
(b) Find the probability that we end with a “head” on the coin.
Answers: (a)
Cherveny
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52
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(b)
12
52
Oct 17
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Math 1004: Probability
Practice
1. Twenty percent of the library books in the fiction section are
worn out. Ten percent of the nonfiction holdings are worn
out. The library’s holdings are 40% fiction and 60%
nonfiction. Use a tree diagram to find the probability that a
book chosen at random from this library is worn out.
2. Color blindness is a gender-linked inherited condition that is
much more common among men than women. Suppose that
5% of all men and 0.4% of all women are color-blind. A
person is chosen at random and found to be color-blind.
What is the probability that the person is male?
3. In a carnival game, a player tosses a coin at most five times.
The player wins as soon as the number of heads exceeds the
number of tails and loses as soon as three tails have been
tossed. Use a tree diagram for this game to calculate the
probability of winning.
Cherveny
Oct 17
Math 1004: Probability
Practice Answers
1. P(worn out) = (.4)(.2) + (.6)(.1) = .14
2. See next class warm-up.
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3. P(win) = 12 + 12 + 12 +
Cherveny
Oct 17
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Math 1004: Probability