Download 2-2 Distributive Property

12-2 Conditional Probability
5/11/17
Conditional Probability: a type of probability that contains a
condition which limits the sample space for an event. They are
written P(B | A) and are read as “the probability of event B,
given event A”. You will see some of these in chart form:
Book classification at a
local library
Illustrated
(I)
Non- (NI)
illustrated
Hardback
(H)
420
780
Nonfiction (NF) 590
250
Paperback Fiction (F)
150
(P)
Nonfiction (NF) 110
430
Fiction (F)
880
What is the probability that a book selected at random is a
paperback, given that it is illustrated? P(P | I)
260/1270
What is the probability that a book selected at random is nonfiction,
given that it is a non-illustrated hardback? P(NF | NIH)
250/1030
A selection of Andrew
McCutchen’s stats from
2012 & 2013. Find each
conditional probability.
P(HR | 2012 hit) = 31/194
P(2013 3B | 3B) = 5/11
2012
2013
Hits
194
185
2B
29
38
3B
6
5
HR
31
21
Some problems will be in word problem form, and it may
appear that you have limited information. You can still
answer questions about conditional probability using the
Conditional Probability Formula
Always the smaller chance.
P(B | A) = P(A and B)
P(A)
The condition; the “given”.
80% of an airline’s flights depart on schedule. 72% of
its flights depart and arrive on schedule. Find the
probability that a flight that departs on time will also
arrive on time. (P(A) is departure…)
P(B | A) = .72 = .90 or 90%
.80
P(B | A) = P(A and B)
P(A)
Let’s find the probability that
McCutchen’s next hit is a 2B. In
other words, the P(2B | Hit).
P(2B | Hit) = P(Hit and 2B)
P(Hit)
As of 5/11/17 his P(Hit and 2B) is .0413
P(Hit) is .215
.0413 ÷ .215 = .1922 or about a 19% chance
that his next hit is a 2B
When using this
formula, the smaller %
always goes on top!
Some problems will need to be solved with a tree diagram.
Bo DeNardo, student of meteorology, makes the following observations:
28% of the time, the sky is “mostly clear”
During the “mostly clear” days, it rained 4% of the time
During the cloudy days, it rained 31% of the time
.04
Rain
.96
No rain
Clear
.28
.31
.72
Cloudy
Rain
What is the probability that a day will
start out clear, but then it will rain?
.28 • .04 = 1.12% or about 1%
What is the probability that a day will
be cloudy, but not rain?
.72 • .69 = 49.68% or about 50%
.69
No rain
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