A British coin has a portrait of Queen Elizabeth $II$ on the 'Heads' side and 'ONE POUND' written on the 'tails' side, while an Indian coin has a portrait of Mahatma Gandhi on the 'Heads' side and '$10$ RUPEES' written on the 'tails' side.
These two coins are tossed simultaneously twice in sucession. The result of the first toss was 'heads' for both the coins. What is the probability that the result of second toss had a '$10$ RUPEES' side.
I wonder what is the relation between the first toss and second toss. I think the probabilty is $\frac{1}{2}$. Is it correct?
intuitively, the coins are not connected, so you want to say the coins are independent, and so are the individual tosses, i.e. tossing the same coin a couple of times, the outcomes are independent as well.
There is only one coin on which it depends if you get 10 rupees or not -- the Indian one, and assuming it is fair, the outcomes are equally weighted, so each has a probability of $1/2$ as you write.