SOLUTION: In a certain college town, 26.8 percent of the students failed Mathematics (Math), 16.4 percent failed Biology (Bio), and 10.9 percent failed both Math and Bio. A student is

Question 778643: In a certain college town,
26.8
percent of the students failed Mathematics (Math),
16.4
percent failed Biology (Bio), and
10.9
percent failed both Math and Bio. A student is sele
cted at random. Let A represent the event of failin
g Math, so that A' is the
probability of passing Math. Let B be the event of
failing Bio and B' the event of passing Bio
If the student failed Bio, what is the probability
that he or she passed Math?
Found 2 solutions by psbhowmick, stanbon:
Answer by psbhowmick(878) (Show Source): You can put this solution on YOUR website!
15.9% failed only in Math
5.5% failed only in Bio

Use the formula for rule of addition of probabilities
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
In a certain college town,
26.8
percent of the students failed Mathematics (Math),
16.4
percent failed Biology (Bio), and
10.9
percent failed both Math and Bio. A student is sele
cted at random. Let A represent the event of failin
g Math, so that A' is the
probability of passing Math. Let B be the event of
failing Bio and B' the event of passing Bio
If the student failed Bio, what is the probability
that he or she passed Math?
-------
P(passed Math |failed Bio) = P(A' AND B)/P(B Bio)
-------
P(A' | B) = (16.4-10.9)/16.4 = 5.5/16.4 = 0.3354
========
Cheers,
Stan H.
=========
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