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 is successful, then the probability that she studied for 4 hours is

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

Answer 1

The correct option is B $\frac{7}{12}$

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.

Using Bayes Theorem we get the required probability.