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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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

$N [p a s s e d m a t h or c h e m] = N [p a s s e d m a t h] + N [p a s s e d c h e m] - N [p a s s e d m a t h & c h e m]$ $N[passed math or chem] = N[passed math] + N[passed chem] - N[passed math & chem]$

Plug in the given values and we have

$90 = 75 + 85 - N [p a s s e d m a t h & c h e m]$ $90 = 75 + 85 - N[passed math & chem]$ ,
so
$N [p a s s e d m a t h & c h e m] = 75 + 85 - 90 = 70$ $N[passed math & chem] = 75 + 85 - 90 = 70$
Hence the required probability is

$P [p a s s e d m a t h ∣ p a s s e s c h e m]$ $P[passed math | passes chem]$
$= \frac{N [p a s s e d m a t h & c h e m]}{N [p a s s e d c h e m]}$ $= (N[passed math & chem]) / (N[passed chem])$
$= \frac{70}{84}$ $= 70/84$
$= \frac{14}{17}$ $= 14/17$

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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?

1 Answer

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