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  • Let the probability of getting head for a biased coin be . It is tossed repeatedly until a

Let the probability of getting head for a biased coin be \frac{1}{4}. It is tossed repeatedly until a head appears. Let \mathrm{N}  be the number of tosses required. If the probability that the equation 64 x^{2}+5 N x+1=0 has no real root is \frac{p}{q}, where p and q are co-prime, then q-p is equal to______.

Option: 1

27


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

64 \mathrm{x}^{2}+5 \mathrm{Nx}+1=0

\mathrm{D}=25 \mathrm{~N}^{2}-256<0

\Rightarrow \mathrm{N}^{2}<\frac{256}{25} \Rightarrow \mathrm{N}<\frac{16}{5}

\therefore \mathrm{N}=1,2,3

\therefore$ 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}

\therefore q-p=27

Posted by

Ritika Jonwal

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