A bag contains 19 unbiased coins and one coin with head on both...

A bag contains 19 unbiased coins and one coin with head on both sides. One coin drawn at random is tossed and head turns up. If the probability that the drawn coin was unbiased, is

\frac{\mathrm{m}}{\mathrm{n}}, \operatorname{gcd}(\mathrm{m}, \mathrm{n})=1

, then

\mathrm{n}^2-\mathrm{m}^2

is equal to :

Options

Correct answer

A. 80

Step-by-step solution

\begin{aligned} & \text{ Required probability }=\frac{\frac{19}{20} \times \frac{1}{2}}{\frac{19}{20} \times \frac{1}{2}+\frac{1}{20} \times 1}=\frac{19}{21} \\ & \therefore \frac{\mathrm{ m}}{\mathrm{n}}=\frac{19}{21} \\ & \Rightarrow \mathrm{n}^2-\mathrm{m}^2=441-361=80\end{aligned}

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