Please note for conditional probabilities I gave you 2 formulas. One deals with
probabilities of events, the other deals with numbers in an event.
)
(
()
(
PB
PA
(Α ∩
Α)=
Ν(Α ∩Β)
Ν(Α)
This 2
nd
formula can be useful for some problems. It is particularly helpful for
combination problems.
HOWEVER, AN ALTERNATIVE APPROACH USES LOGIC.
Example: Problem set problem 4a)
The question asks what is the conditional probability of getting a black ball on the second
draw given the first ball is black. Since there are only 2 black balls, there is only 1 way to
get a black ball on the 2
nd
draw given the first draw was black. Also, since we already
drew one ball there are only 4 balls left. Therefore, our conditional probability is ¼.
Remark: This approach works nicely in cases of drawing without replacement (whether
that is balls from a box or letters from a string).
Note: If we wanted the probability of 1
st
draw black and 2
nd
draw black; we would use
the total probability rule.
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 Spring '08
 MARTIN
 Conditional Probability, Probability, Probability theory, Probability space, Hunter Green

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