If two fair coins are flipped and at least one of the outcomes is known to be a head, what is the probability that both outcomes are heads?

If the difference between the expectation of the square of a random variable $$\left( {E\left[ {{X^2}} \right]} \right)$$ and the square of the expectation of the random variable $${\left( {E\left[ X \right]} \right)^2}$$ is denoted by R then

A sample space has two events A and B such that probabilities $$P\,(A\, \cap \,B)\, = \,1/2,\,\,P(\overline A )\, = \,1/3,\,\,P(\overline B )\, = \,1/3$$.
What is P $$P\,(A\, \cup \,B)\,$$?

Suppose there are two coins. The first coin gives heads with probability 5/8 when tossed, while the second coin gives heads with probability 1/4. On e of the two coins is picked up at random with equal probability and tossed. What is the probability of obtaining heads?