Answer:
a) 60% probability that he picks up a blue pen and recognizes it as blue.
b) 62.5% probability that he chooses a pen and thinks it is blue.
c) 96% probability that he actually chose a blue pen.
Step-by-step explanation:
The problem has the following probabilities:
75 of 100 pens are blue, so a 75% probability that a pen is blue.
25 0f 100 pens are green, so a 25% probability that a pen is green.
If a pen is blue, an 80% probability that he thinks it is a blue pen
If a pen is blue, a 20% probability that he thinks it is a green pen.
If a pen is green, a 90% probability that he thinks it is a green pen.
If a pen is green, a 10% probability that that he thinks it is a blue pen.
a) (3pts) What is the probability that he picks up a blue pen and recognizes it as blue?
75% probability he picks up a blue pen.
80% that he recognizes a blue pen as blue.
60% probability that he picks up a blue pen and recognizes it as blue.
b) (3 pts) What is the probability that he chooses a pen and thinks it is blue?
75% probability that he picks up a blue pen.
80% that he recognizes a blue pen as blue.
25% probability that he picks up a green pen
10% probability that he thinks a green pen is blue.
62.5% probability that he chooses a pen and thinks it is blue.
c) (4pts) Given that he thinks he chose a blue pen, what is the probability that he actually chose a blue pen?
62.5% probability that he thinks that he choose a blue pen.
60% probability that he chooses a blue pen and think that it is blue.
96% probability that he actually chose a blue pen.