Question

A jee aspirant estimates that she will be successful with an 80% chance if she studies 10 hours per day, with a 60% chance if she studies 7 hours per day and with a 40% chance if she studies 4 hours per day. She further believes that she will study10 hours, 7 hours and 4 hours per day with probabilities 0.1, 0.2 and 0.7 respectively
Given that she does not achieve success, the probability she studied for 4 hours is

• A. $\frac{18}{26}$
  
• B. $\frac{19}{26}$
  
• C. $\frac{20}{26}$
  
• D. $\frac{21}{26}$

Answer 1

Answer: (D)

$\frac{21}{26}$

A jee aspirant estimates that she will be successful with an 80% chance if she studies 10 hours per day, with a 60% chance if she studies 7 hours per day and with a 40% chance if she studies 4 hours per day. She further believes that she will study10 hours, 7 hours and 4 hours per day with probabilities 0.1, 0.2 and 0.7 respectively
A : She get a success
t : She studies 10 hrs : P (T) = 0.1
S : She studies 7 hrs : P (S) = 0.2
F : She studies 4 hrs : P (F) = 0.7

$P=\frac{A}{T}=0.8$;

P$\frac{A}{S}=0.6$; P$\frac{A}{F}=0.4$

Now, $P\left(A\right)=P(A\cap T)+P(A\cap S)+P(A\cap F)$

$=P\left(T\right).P\frac{A}{T}+P\left(S\right).P\frac{A}{s}+P\left(F\right).P\frac{A}{f}$
$=\left(0.1\right)\left(0.8\right)+\left(0.2\right)\left(0.6\right)+\left(0.7\right)\left(0.4\right)$
$=0.08+0.12+0.28=0.48$
$P\frac{F}{A}=\frac{P(F\cap A)}{P\left(A\right)}=\frac{\left(0.7\right)\left(0.4\right)}{0.48}=\frac{0.28}{0.48}=\frac{7}{12}$
$P\frac{F}{\overline{A}}=\frac{P(F\cap \overline{A})}{P\left(\overline{A}\right)}=\frac{P\left(F\right)-P(F\cap A)}{0.52}$
$=\frac{\left(0.7\right)-0.28}{0.52}=\frac{0.42}{0.52}=\frac{21}{26}$