Download Chapter 15: Probability Rules!

Chapter 15: Probability
Rules!
Ryan Vu and Erick Li
Period 2
Terms
● Sample Space The collection of all possible outcome values. The sample
space has a probability of 1.
● Disjoint events Two events are disjoint (or mutually exclusive) if they
have no outcomes in common.
● Addition Rule If A and B are disjoint events, then the probability of A or B
is P(A∪B) = P(A) + P(B).
● General Addition Rule For any two events, A and B, the probability of A
or B is P(A∪B) = P(A) + P(B) - P(A∩B).
● Conditional probability P(B|A) = P(A∩B) / P(A) ;P(B|A) is read “the
probability of B given A.”
● Independence (used casually) Two events are independent if knowing
whether one event occurs does not alter the probability that the other event
occurs.
Terms
● Multiplication Rule If A and B are independent events, then the
probability of A and B is P(A∩B) = P(A) × P(B).
● General Multiplication Rule For any two events, A and B is P(A∩B) =
P(A) × P(B|A).
● Independence (used formally) Events A and B are independent when
P(B|A) = P(B).
● Tree diagram A display of conditional events or probabilities that is helpful
in thinking through conditioning
Problem 11; Page 363
a) P(P∩C) = .11
b) P(P) = .11 + .16 = .27
c) P(C|P) = P(C∩P) / P(P) = .11 / (.11 + .16) = .4074
d) P(P|C) = P(P∩C) / P(C) = .11 / (.11 + .21) = .3438
Problem 13; Page 364
a) P(18∩C) = outcome(18∩C) / outcome(all) = 135 / 1005 =
.1343
b) P(C|18) = outcome(C∩18) / outcome(18) = 135 / 217 =
.6221
c) P(18|C) = outcome(18∩C) / outcome(C) = 135 / 437 =
.3089
d) P(65|B) = outcome(65∩B) / outcome(B) = 92 / 518 = .1776
Problem 13; Page 364
e) P(B|65) = outcome(B∩65) / outcome(65) = 92 / 167 =
.5509