Download 7-4

Math 310
Section 7.4
Probability
Odds
Def
Let P(A) be the probability that A occurs and P(Ā)
be the probability that A does not occur. Then
the odds in favor of an event A are:
P(A)/P(Ā) or P(A)/(1-P(A))
The odds against are P(Ā)/P(A).
Odds again
In terms of equally likely outcomes:
Odds in favor = Number of favorable outcomes
Number of unfavorable outcomes
Odds against = Number of unfavorable outcomes
Number of favorable outcomes
Notation
Often a colon is used instead of a fraction:
Odds in favor 4/3 or 4:3
Odds against 3/4 or 3:4
Probability from odds
Thrm
If the odds in favor of event E are m : n then
P(E) = m/(m + n)
If the odds against E are m : n then
P(E) = n/(m + n)
Ex.
What are the odds in favor of rolling a number
greater than 4 on a die?
2 : 4 or 1:2
Ex.
What are the odds of throwing a tails on a penny?
1:1
Ex.
What are the odds of drawing a 2 or a 3 from a 52
card deck?
8 : 44 or 2 : 11
Conditional Probability
Conditional probability is the probability of a
sequence of events occurring given that one or
more events in the sequence is guaranteed to
occur.
Conditional Probability
Thrm
If A and B are events in a sample space S and
P(A) ≠ 0, then the conditional probability that
event B occurs given that event A has occurred
is given by
P(B|A) = P(A ∩ B)
P(A)
The Idea
The basic idea for conditional probability is that by
adding more information we reduce the sample
space.
Ex.
What is the probability of rolling a 2 if you know
the roll is a prime number?
S = {1, 2, 3, 4, 5, 6}, A = {2}
But if we know the roll is a prime then
S* = {2, 3, 5}. So the P(A) = 1/3