JEE Mains · Maths · STD 12 - 13. probability
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 :
- A 80
- B 60
- C 72
- D 64
Answer & Solution
Correct Answer
(A) 80
Step-by-step Solution
Detailed explanation
\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…
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