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

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