Download The Practice of Statistics Third Edition Chapter 6

Daniel S. Yates
The Practice of Statistics
Third Edition
Chapter 6:
Probability and Simulation:
The Study of Randomness
Copyright © 2008 by W. H. Freeman & Company
Ex. What is the sample space for the roll of a die?
s= {1,2,3,4,5,6} All equal probability
What is the sample space for the roll of a pair of dice?
s={2,3,4,5,6,7,8,9,10,11,12} different probability
• Tree diagrams help to determine the sample space
• Ex. An experiment consists of flipping a coin and
tossing a die.
• Ex. For your dinner you need to choose from six entrees,
eight sides, and five desserts. How many different combinations
of entrée, side and dessert are possible?
6x8x5 = 240
Disjoint (mutually exclusive events)
Ex. Complementary events
What is the probability of rolling a five when a pair of dice are
rolled?
P(A) = 4/36 = .111 =11.1%
• Independent Events – two events are independent if
the occurrence of one event does not change the
probability that the other occurs.
Ex. What is the probability of rolling a 7 each of three
consecutive roles of a pair of dice?
P(rolling 7) = 6/36 = 1/6 ; P( three 7s) = (1/6)3 =0.5%
Ex.
Event A = { a household is prosperous; Inc. > 75 k}
Event B = { a household is educated; completed
college}
P(A) = 0.125
P(A and B) = 0.077
P(B) = 0.237
What is the probability the household is either
prosperous or educated?
P (A or B) = P(A) + P(B) – P(A and B) = 0.125 + 0.237 –
0.077
= 0.285
• Conditional probability - The probability of the occurrence
of an event given that another event has occurred.
♣ Notation – P(B|A) > probability of B given A
Ex.
A die has sides 1,2,3 painted red and sides 4,5,6
painted blue.
Event A = {Roll Blue}
Event B = {Roll Red}
Event C = {Roll even}
Event D = {Roll Odd}
What is the probability that you roll an even given
we rolled a blue?
What is the probability of rolling a red, even?
What is the probability that you roll an odd given
you rolled a blue?
• General Multiplication rule can be extended for any number
of events.
P(A and B and C) = P(A) x P(B|A) x P(C|A and B)