A boy has color blindness and has trouble distinguishing blue and green. There are 60 blue pens and 40 green pens mixed together in a box. Given that he picks up
a blue pen, there is a 60% chance that he thinks it is a blue pen and a 40% chance that he thinks it is a green pen. Given that he picks up a green pen, there is an 80% chance that he thinks it is a green pen and a 20% chance that he thinks it is a blue pen. Assume that the boy randomly selects one of the pens from the box.

a. What is the probability that he picks up a blue pen and recognizes it as a blue pen?

b. What is the probability that he chooses a pen and thinks it is blue?

c. Given that he thinks he chose a blue pen, what is the probability that he actually chose a blue pen?