Question

Given a fair coin, if the coin is flipped n times, what is the probability that heads is only tossed on odd numbered tosses. (tails could also be tossed on odd numbered tosses)

Answer 1

According to the question, if Head comes, it will appear on 1st, 3rd, 5th....tosses.

But it’s not strictly given that on odd tosses, only Head can appear. Which means, on even tosses only Tail can appear however in odd tosses, both Head and tail can appear. So main restriction is on even no of tosses. Now if n is even, there must be (n/2) even places and if n is odd, there will be (n-1)/2 even places. So P(H is only tossed in odd no of tosses) = (P(T))n/2 if n is even = (0.5)n/2, if n is even

= (P(T))(n-1)/2 if n is odd = (0.5)(n-1)/2. , if n is odd.