Let the probability of getting head for a biased coin be 1/4. It is tossed repeatedly until a head appears. Let N be the number of tosses required. If…

Question

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

MARKS Content Team · Accepted Answer

Correct answer: 27. Given a quadratic equation 64x^2+5nx+1=0 has no real roots, so D<0 ⇒25N^2-4×64<0 ⇒N<16/5⇒N=1,2,3 And, For a biased coin, the probability of getting head is P=1/4, and probability of getting tail will be Q=3/4 So, required probability is 1/4+3/4·1/4+34^2·1/4+34^3·1/4=p/q ⇒(141-34^3)/(1-34)=p/q ⇒1-34^3=p/q ⇒1-27/64=p/q ⇒p/q=37/64 q-p=27

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