Christine has always been weak in mathematics. Based on her performance prior to
ID: 3441019 • Letter: C
Question
Christine has always been weak in mathematics. Based on her performance prior to the final exam in Calculus, there is a 49% chance that she will fail the course if she does not have a tutor. With a tutor, her probability of failing decreases to 19%. There is only a 59% chance that she will find a tutor at such short notice.
What is the probability that Christine fails the course? (Round your answer to 4 decimal places.)
Christine ends up failing the course. What is the probability that she had found a tutor? (Round your answer to 4 decimal places.)
a.What is the probability that Christine fails the course? (Round your answer to 4 decimal places.)
Explanation / Answer
a)
Let
F = she fails
T = she finds a tutor
By Bayes' Rule,
P(F) = P(T) P(F|T) + P(T') P(F|T')
= 0.59*0.19 + (1-0.59)*(0.49)
= 0.3130 [answer]
************
b)
P(T|F) = P(T n F) / P(F)
As
P(T n F) = P(T) P(F|T) = 0.59*0.19 = 0.1121
Then
P(T|F) = 0.1121/0.313 = 0.358146965 = 0.3581 [answer]
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