Question

Given that she is successful, the chance she studied for 4 hours, is

• A. $\frac{6}{12}$
• B. $\frac{7}{12}$
• C. $\frac{8}{12}$
• D. $\frac{9}{12}$

Answer 1

Answer: (B)

$\frac{7}{12}$

Given,The probability of a Jee Aspirant to be successful if he studies for 10 hours per day,$P\left(t_{10}\right)=0.8$
The probability of a Jee Aspirant to be successful if he studies for 7 hours per day,$P\left(t_7\right)=0.6$
The probability of a Jee Aspirant to be successful if he studies for 4 hours per day,$P\left(t_4\right)=0.4$
The probability that she will study 10 hours per day,$P\left(A\right)=0.1$
The probability that she will study 7 hours per day,$P\left(B\right)=0.2$
The probability that she will study 4 hours per day,$P\left(C\right)=0.7$
$\therefore Theprobabilitythatshewillbesuccessful,P\left(S\right)=P\left(t_{10}\right)\ast P\left(A\right)+P\left(t_7\right)\ast P\left(B\right)+P\left(t_4\right)\ast P\left(S/t_4\right)$
$=0.8\ast 0.1+0.6\ast 0.2+0.4\ast 0.7=0.48$
But probability that she studies 4 hours per day for success=$P(t_4\cap C)=P\left(t_4\right)P\left(C\right)=0.4\ast 0.7=0.28$
Since $(A,t_{10}),(B,t_7),(C,t_4)$ pairwise independent $\Rightarrow P(A\cap B)=P\left(A\right).P\left(B\right)$
$\therefore$ The probability that she studies 4 hours per day given she is successful,$P\left(C/S\right)=\frac{P(C\cap S)}{P\left(S\right)}$
$=\frac{0.28}{0.48}=\frac{7}{12}$