Three fair coins are tossed. What is the probability that

Question

Three fair coins are tossed. What is the probability that they are all heads if the first coin is head?

I am stuck after writing down $P(3H|FirstHead)=\frac{P(FirstHead|3H)P(3H)}{P(FirstHead)}$

P(FirstHead) = ? $({3\choose1} (1/2)(1/2)^2)$

P(3H) = ? $(1/2)^3$

So confusing, can't get any further. How can we approach it ?

Answer 1

These are all independent events.

So, the first coin being a head has no effect on the other two coins being heads. That being said, the probability of all three being heads given the first is a head, is simply the probability that the last two are heads.

This happens with probability $\displaystyle \frac{1}{4}$.