The coin we choose is equally likely to be fair or unfair, since the ratio of fair to unfair coins is 2:2 = 1:1.
So, 50% of the times we pick a fair coin, which lands on heads with probability 50%.
The other 50% of the times we pick an unfair coin, which lands on heads with probability 90%.
Since these two events are mutually exclusive (a coin is either fair or unfair), the probability of having the coin to land on heads is
[tex] \underbrace{0.5\times 0.5}_{\text{fair coin lainding on heads}} + \underbrace{0.5\times 0.9}_{\text{unfair coin lainding on heads}} = 0.25 + 0.45 = 0.65 [/tex]
