1. (12pts) A boy has color blindness and has trouble distinguishing blue and gre
ID: 3044664 • Letter: 1
Question
1. (12pts) 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 70% chance that he thinks it is a blue pen and a 30% chance that he thinks it is a green pen. Given that he picks 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) (4pts) What is the probability that he picks up a blue pen and recognizes it as blue? b) (4pts) What is the 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?Explanation / Answer
a)P(picks blue and recognise as blue) =P(pick blue)*P(recognise blue|pick blue) =(60/100)*0.7=0.42
b) P(recongnise as blue)=P(pick blue)*P(recognise blue|pick blue)+P(pick green)*P(recognise blue|pick green)
=(60/100)*0.7+(40/100)*0.2=0.5
c)
P(blue pen |recongnise as blue) =P(pick blue)*P(recognise blue|pick blue)/P(recognise blue)
=(60/100)*0.7/0.5 =0.84
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