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In a certain college, 25% of students failed mathematics, 15% failed computer science. There is a 40% chance that a student failed computer science given that they failed mathematics.

  1. Find the probability that the student failed both mathematics and computer science.

How would I go about doing this problem?

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  • $\begingroup$ google bayes' theorem $\endgroup$
    – Scavenger23
    Mar 15, 2017 at 12:54
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    $\begingroup$ Hint: try it wth actual numbers. Suppose there were $1000$ students in total? How many failed math? How many failed both? $\endgroup$
    – lulu
    Mar 15, 2017 at 13:00

3 Answers 3

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complete a probability table - what we know 

              M    M'
       C      ?    ?    85

       C'     ?    ?    15
              75   25

(25% failed maths, and 40% of those failed computers, making 10% of all people failed both)

the rest can be filled in

               M    M'
        C      70   15    85

        C'     5    10    15
               75   25
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If you are unsure how to fill a table in like Catos above, it results from for example solving the following linear equation system.

$$\begin{array}{cccc|c}MC&M'C&MC'&M'C'&rhs\\\hline1&1&0&0&0.85\\0&0&1&1&0.15\\1&0&1&0&0.75\\0&1&0&1&0.25\end{array}$$

but the table and the equations may be different for your particular problem.

How to read it: "The sum of $MC$ and $M'C$ is 85%" et.c.

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Given two events $A$ and $B$, the conditional probability is $$ P(A|B) = \dfrac{P(AB)}{P(B)} $$

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