Joseph is deciding whether he's taking medicine or engineering
course. The probability that he's choosing enginireeng is 65 %,
while the probability that he's going to pass the Board Exam in
Medicine is 89% and in Engineeirng is 69%.
a.) what is the probability that Joseph will
pass the course?
b.) If Joseph doesn't pass the
exam, waht is the probability that
he choose Medicine?
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a.) what is the probability that Joseph will
pass the course?
P(MP,EP) = P(MP) + (EP)
= .76
= 76%
the probability of M or E, if the *this phrase means that one
events are *mutually exclusive, events taking place prevents
may be found by adding the other event from taking
probabilities. place.
2

b.) If Joseph doesn't pass the exam,
what is the probability that he
choose Medicine?
this is an example of a
P(N/M) = P(MN)
bayes' formula: It is used
P(MN) + P(EN)
to find the conditional
probability of Event M
= 0.0385
occuring, given that Event
(0.0385) + (.2015)
N has already occurred.
= 0.16 or 16%
probability = number of favorable outcome
total possible outcome
3

and this is the tree diagram.
P .89 P(MP) = .3115
M
N.11 P(MN)= .0385
P .69 P(EP)=.4485
F
N .31 P(EN)=.2015
4