Question

a coin is weighted deliberately so that the probability of tossing heads is twice the probability of tossing tails. what is the probability of tossing three heads in a row? what is the probability of tossing three tails in a row? what is the relative probability of tossing three heads versus three tails?

Answer 1

Here we are given that a coin is weighted in such a manner that the probability of tossing a head is twice than tossing a tail, so p(h) =2p(t) and p(h) +p(T) =1 so it implies by putting value 2p(t)+p(t)=1 and then p(T) =1/3 and p(h) =2/3.

Now we are to find p(3 head in a row) = (2/3)^3=8/27.

And probability of 3 tail is (1/3)^3=1/27

Now relative of head versus tail is (8/27)/(1/27)=8