Students and exam

In a certain college, accounting is one of the courses. Among the accounting students, 60% are male. Among the male students, 75% passed the exams, while among the female students, 50% failed.
(a) Present this information using a probability tree diagram.
(b) Determine the probability that an accounting student selected at random passed the exams.
(c) An accounting student is selected at random. Find the probability that it is a male student.
(d) An accounting student who failed the exam is selected. Determine the probability that she is female.

Final Answer:

b =  0.65
c =  0.6
d =  0.875

Step-by-step explanation:

$$\begin{gathered} m=60\%=\frac{60}{100}=\frac{3}{5}=0.6 \\ f=1-m=1-0.6=\frac{2}{5}=0.4 \\ b=m\cdot 0.75+f\cdot (1-0.50)=0.6\cdot 0.75+0.4\cdot (1-0.50)=0.65 \end{gathered}$$

$c=m=0.6$

$$\begin{gathered} P(A\cap B)=P(A)P(B|A)=P(B)P(A|B) \\ d=\frac{m\cdot 0.25+f\cdot 0.50}{f}=\frac{0.6\cdot 0.25+0.4\cdot 0.50}{0.4}=0.875 \end{gathered}$$

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