6. A boy has color blindness and has trouble distinguishing blue and green. There are 75 blue pens and 25 green pens mixed together in a box. Given that he picks up a blue pen, there is g 80% chance that he thinks it is a blue pen and a 20% chance that he thinks it is a green pen. Given that he picks a green pen, there is an 90% chance that he thinks it is a green pen and a 10% 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 blue? 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? 7. A and B are events such that P(A) = 0.4 and P (A U B) = 0.5. Find P(B) in each of the following cases. a) A and B are mutually exclusive b) A and B are independent c) P(A | B) = 0.2 d) P (An B) = 0.15