A fair coin is tossed 10 times. If the probability that heads never occur on consecutive tosses be (p/g) where p and q are relatively prime positive integers then find the value of (q-7 p).

Question

A fair coin is tossed 10 times. If the probability that heads never occur on consecutive tosses be (p/g) where p and q are relatively prime positive integers then find the value of (q-7 p). (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Probability =( 6 C 5+ 7 C 4+ 8 C 3+ 9 C 2+ 10 C 1+1/910)=(9/64) (Gap method)

Q. A fair coin is tossed 10 times. If the probability that heads never occur on consecutive tosses be $\frac{p}{g}$ where $p$ and $q$ are relatively prime positive integers then find the value of $(q - 7 p)$ .

Probability $= \frac{^{6} C _{5} + ^{7} C _{4} + ^{8} C _{3} + ^{9} C _{2} + ^{10} C _{1} + 1}{9 ^{10}} = \frac{9}{64}$ (Gap method)

Q. A fair coin is tossed 10 times. If the probability that heads never occur on consecutive tosses be gp​ where p and q are relatively prime positive integers then find the value of (q−7p).

Probability =9106C5​+7C4​+8C3​+9C2​+10C1​+1​=649​ (Gap method)

Q. A fair coin is tossed 10 times. If the probability that heads never occur on consecutive tosses be $\frac{p}{g}$ where $p$ and $q$ are relatively prime positive integers then find the value of $(q - 7 p)$ .

Probability $= \frac{^{6} C _{5} + ^{7} C _{4} + ^{8} C _{3} + ^{9} C _{2} + ^{10} C _{1} + 1}{9 ^{10}} = \frac{9}{64}$ (Gap method)