Question

A student has managed to enter in Harward University. It was informed that the probability of getting a scholarship is $40 \%$. In case of getting it, the probability of completing the course is 0.8 , while in the case of not getting the scholarship, the probability is only 0.4 . If after some years from now, you meet the student, completing his course from Harward, the probability that he was given the scholarship, is

• A. $\frac{8}{17}$
• B. $\frac{4}{7}$
• C. $\frac{8}{15}$
• D. $\frac{4}{9}$

Answer 1

Answer: (B)

E : student completed the course

$P ( S / E ) =\frac{ P ( S \cap E )}{ P ( E )}=\frac{ P ( S ) \cdot P ( E / S )}{ P ( S ) \cdot P ( E / S )+ P (\overline{ S }) \cdot P ( E / \overline{ S })} $
$ =\frac{(0.4)(0.8)}{(0.4)(0.8)+(0.6)(0.4)}$
$=\frac{0.32}{0.32+0.24}=\frac{32}{56}=\frac{4}{7}$