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