5.3 Conditional Probability
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Transcript of 5.3 Conditional Probability
5.3 Conditional ProbabilityObjectives:By the end of this section, I will beable to…
1) Calculate conditional probabilities.2) Recognize the difference between sampling
with replacement and sampling without replacement.
CONDITIONAL PROBABILITY:
• For two RELATED events A and B, the probability of B given A.
P(B|A)
CONDITIONAL PROBABILITY:
• Key words: GIVEN, KNOWING, IFDIVIDE if you see these key words!
𝑝 (𝐵∨𝐴 )=𝑝 (𝐴∩𝐵)𝑝 (𝐴)
Cheating Hearts1) The probability that a Sallies student
cheats on his girl is 0.79. If the probability that a Sallies boy and his girl both cheat is 0.14, what is the probability that his girl cheats GIVEN that he cheats?0.14 0.1772 0.18
0.79
Pretty Boys2) Eighty-four percent of Sallies boys think they are
good looking. Nine percent of Sallies boys think
they are good looking and actually are cute. If a
student is selected at random, what it the
probability that this person is actually good
looking? 0.09 0.1071 0.110.84
Rich girls3) Evan has dated a lot of girls and 21%
were rich. 12% of them were rich and
pretty at the same time. If one of his
dates is chosen at random, what it the
probability that this girl is pretty?
0.12 0.5714 0.570.21
Two-way Table
• Make a two way table to help you organize information.
Who? Who? TOTALWhat?
What?
TOTAL
Question: Do you have your own car?
Two-way Table
Male Female TOTALHas a car
Doesn’t have a car
TOTAL
Question: Do you have your own car?
P(car) =
P(car | male) =
P(No car | female) =
P(male | no car) =
HINTS• DIVIDE for the key words of
GIVEN IF KNOWING KNOW
• Bigger decimal/percentage always goes in the denominator