Question

Given that she does not achieve success, the probability she studied for 4 hours is

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

$\text{A:She get a success}\text{T: She studies 10 hrs : P (T)=0.1}\text{She studies 7 hrs : P (S)=0.2}\text{She studies 4 hrs : P (F)=0.7}$

$P\left(A/T\right)=0.8;P\left(A/S\right)=0.6;P\left(A/F\right)=0.4Now,P\left(A\right)=P(A\cap T)+P(A\cap S)+P(A\cap F)=P\left(T\right).P\left(A/T\right)+P\left(S\right).P\left(A/S\right)+P\left(F\right).P\left(A/F\right)=\left(0.1\right)\left(0.8\right)+\left(0.2\right)\left(0.6\right)+\left(0.7\right)\left(0.4\right)=0.08+012+0.28=0.48P\left(F/A\right)=\frac{P(F\cap A)}{P\left(A\right)}=\frac{\left(0.7\right)\left(0.4\right)}{0.48}=\frac{0.28}{0.48}=\frac{7}{12}P\left(F/\overline{A}\right)=\frac{P(F\cap \overline{A})}{P\left(\overline{A}\right)}=\frac{P\left(A\right)-P(F\cap A)}{0.52}=\frac{\left(0.7\right)-0.28}{0.52}=\frac{0.42}{0.52}=\frac{21}{26}$