6A fair coin is to be tossed until a head comes up for the f

(6)A fair coin is to be tossed until a head comes up for the first time. What are the chances of happening on an even-numbered toss?

Solution

P=(0.5*0.5)+(0.5*0.5*0.5*0.5)+(0.5*0.5*0.5*0.5*0.5*0.5)+........... upto infinity

sum of geometric progression with r<1 =a/(1-r)

Here a=0.25, r=0.25

P=0.25/(1-0.25)=1/3=0.333333