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 females, 50% failed.
(a) present this 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
(d)an accounting student who failed the exam. Determine she is female

Correct answer:

b =  0.65
c =  0.6
d =  0.875

Step-by-step explanation:

$$\begin{gathered} m=60\%=\frac{60}{100}=\frac{3}{5}=0.6 \\ f=1-m=1-0.6=\frac{2}{5}=0.4 \\ b=m\cdot 0.75+f\cdot (1-0.50)=0.6\cdot 0.75+0.4\cdot (1-0.50)=\frac{13}{20}=0.65 \end{gathered}$$

$c=m=0.6=\frac{3}{5}$

$$\begin{gathered} P(A\cap B)=P(A)P(B|A)=P(B)P(A|B) \\ d=\frac{m\cdot 0.25+f\cdot 0.50}{f}=\frac{0.6\cdot 0.25+0.4\cdot 0.50}{0.4}=\frac{7}{8}=0.875 \end{gathered}$$

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