PROBABILITY-a very easy yet confusing question?

a crime is committed at the corner of an intersection. it is determined that the perpetrator was wearing a Y sweatpants and a G sweatshirt. a student is arrested who was wearing both of these items of clothes on the evening of the crime. the defense provides evidence that shows the probability that a random selected student in the area wearing Y sweatpants is 1/10.the defense provides evidence that shows the probability that a random selected student in the area wearing G sweatshirt is 1/5. the prosecutor concludes that the probability that a student wearing both y and G is (1/10)(1/5)=1/50=2% which is large enough to cause reasonable doubt for the jury. do you think the prosecutor's claim about the probability is true or false? justify your answer. ume the probabilities, 1/5 and 1/10 is correct.