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Need Solution for R.D.Sharma Maths Class 12 Chapter 30 Probability  Exercise Multiple Choice Questions  Question 49 Maths Textbook Solution.

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Answer:(a)

Hint: You must know the rules of finding probability.

Given: P(A solve problem correctly) = \frac{1}{3}

P(B solve problem correctly) =\frac{1}{4}

Making common errors =\frac{1}{20}

Solution:

\begin{aligned} &\mathrm{E}_{1}=\text { solve correctly } \\ &\mathrm{E}_{2}=\text { solve incorrectly } \\ &A=\text { Obtain same result } \end{aligned}

P\left(\frac{E_{1}}{A}\right)=\frac{P\left(E_{1}\right) P\left(\frac{A}{E_{1}}\right)}{P\left(E_{1}\right) P\left(\frac{A}{E_{1}}\right)+P\left(E_{2}\right) P\left(\frac{A}{E_{2}}\right)}

\begin{aligned} &=\frac{\frac{1}{12} \times 1}{\frac{1}{12} \times 1+\frac{6}{12} \times \frac{1}{20}} \\ &=\frac{20}{26}=\frac{10}{13} \end{aligned}

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