JEE Mains · Maths · STD 12 - 13. probability
Let the probability of getting head for a biased coin be \(\frac{1}{4}\). It is tossed repeatedly until a head appears. Let \(N\) be the number of tosses required. If the probability that the equation \(64 x ^2+5 Nx +1=0\) has no real root is \(\frac{ p }{ q }\), where \(p\) and \(q\) are co-prime, then \(q-p\) is equal to
- A \(27\)
- B \(25\)
- C \(24\)
- D \(26\)
Answer & Solution
Correct Answer
(A) \(27\)
Step-by-step Solution
Detailed explanation
\(64 x ^2+5 Nx +1=0\) \(D =25 N ^2-256 < 0\) \(\Rightarrow N ^2 < \frac{256}{25} \Rightarrow N < \frac{16}{5}\) \(\therefore N =1,2,3\) \(\therefore \text { Probability }=\frac{1}{4}+\frac{3}{4} \times \frac{1}{4}+\frac{3}{4} \times \frac{3}{4} \times \frac{1}{4}=\frac{37}{64}\)…
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