Question

amy,kim, and max took turns flipping an unfair coin with probability of tail 0.3. Amy first, kim second, Max third, army fourth and so on. find the probability that Max flipped the first trials

Answer 1

Max flipped the first tail =P(Amy and Kim tails and Max heads)+P(Amu, Kim,Max,Amy ,Kim heads and then Max flips tails)+...............

=(0.7)^2*0.3+(0.7)^5*0.3+(0.7)^8*0.3+(0.7)^11*0.3+...........

(above is an infinite geometric series for which sum is a/(1-r) where a is first term and r is common ratio)

=(0.7^2)*0.3/(1-0.7^3)=0.2237