SOLUTION: In a college 30% students fail in Physics, 25% fail in Mathematics and 10% students fail in both. One student is chosen at random. What is the probability that a) He fails in Math

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Question 235847: In a college 30% students fail in Physics, 25% fail in Mathematics and 10% students fail in both. One student is chosen at random. What is the probability that
a) He fails in Mathematics if he has failed in Physics
b) He fails in Physics if he has failed in Mathematics.
c) He fails in Physics or Mathematics.

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
In a college 30% students fail in Physics, 25% fail in Mathematics and 10% students fail in both. One student is chosen at random. What is the probability that
a) He fails in Mathematics if he has failed in Physics
P(m|p) = P(m and p)/P(p) = 0.10/0.30 = 1/3
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b) He fails in Physics if he has failed in Mathematics.
P(p|m) = P(p and m)/P(m) = 0.10/0.25 = 10/25 = 2/5
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c) He fails in Physics or Mathematics.
P(p or m) = P(p) + P(m) - P(p and m)
= 0.30 + 0.25 - 0.10 = 0.45
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Cheers,
Stan H.