Question

A question can be solved by $2$ methods. The probability of getting the correct answer using the method I and II are $\frac{1}{7}$ and $\frac{1}{8}$ respectively. If the problem was solved incorrectly then the probability that method I is

• A. $\frac{47}{97}$
• B. $\frac{48}{97}$
• C. $\frac{47}{100}$
• D. $\frac{49}{97}$

Answer 1

The correct option is B $\frac{48}{97}$

Let
$E=$ Event when the problem was solved incorrectly
$E_1=$ problem was solved using method I
$E_2=$ problem was solved using method II
Using Bayes theorem,
$P\left(E_1|E\right)=\frac{P\left(E|E_1\right)P\left(E_1\right)}{P\left(E|E_1\right)P\left(E_1\right)+P\left(E|E_2\right)P\left(E_2\right)}=\frac{48}{97}$