75% students passed math, 85% passed chemistry, and 90% passed math or chemistry. A student is selected at random. What is the probability that the student passed mathematics, given that the student passed chemistry?

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Answer 1 · 2017-04-13T23:35:50

We have that where N=number of students

#N[passed math or chem] = N[passed math] + N[passed chem] - N[passed math & chem] #

Plug in the given values and we have

#90 = 75 + 85 - N[passed math & chem]#,
so
#N[passed math & chem] = 75 + 85 - 90 = 70#
Hence the required probability is

#P[passed math | passes chem] #
#= (N[passed math & chem]) / (N[passed chem]) #
#= 70/84 #
#= 14/17 #