probability: question (III)and (IV)
1) A magician is going to draw one ball that can come from two urns. We don’t know for sure which urn
she will choose. But we know that the balls in the urns can be of red color or blue color and that the
?rst urn has 2 red balls and 4 blue balls and the second urn has 2 red balls and 1 blue ball. Hints: Note now that the number of balls in the two urns is diferent. (I) Make a picture of the probability tree that exempli?es the two uncertain events we are facing in
this example.
(II) Assume that the magician chooses each urn in an equally likely way, i.e., the probability she chooses the ?rst urn is %. (a) What is the probability of taking a red ball if we continue to assume that the the probability
she chooses the ?rst urn is %? (b) Ifwe observe a red ball, what is the probability that it came from um I? Also, continue to
assume the probability she chooses the ?rst urn is $1,.
(c) Ifwe observe a red ball, what is the probability that it came from um 11? Again, continue to
assume the probability she chooses the ?rst urn is %.
she chooses the ?rst urn is %? (b) Ifwe observe a red ball, what is the probability that it came from um I? Also, continue to
assume the probability she chooses the ?rst urn is $1,.
(c) Ifwe observe a red ball, what is the probability that it came from um 11? Again, continue to
assume the probability she chooses the ?rst urn is %.
(III) Assume that the magician chooses the ?rst urn with probabilty equal to i.
(a) What is the probability of taking a red ball if we continue to assume that the the probability she chooses the ?rst urn is :11? (b) Ifwe observe a red ball, what is the probability that it came from um I? Also, continue to
assume the probability she chooses the ?rst urn is i. (c) Ifwe observe a red ball, what is the probability that it came from um 11? Again, continue to
assume the probability she chooses the ?rst urn is i.
(a) What is the probability of taking a red ball if we continue to assume that the the probability she chooses the ?rst urn is :11? (b) Ifwe observe a red ball, what is the probability that it came from um I? Also, continue to
assume the probability she chooses the ?rst urn is i. (c) Ifwe observe a red ball, what is the probability that it came from um 11? Again, continue to
assume the probability she chooses the ?rst urn is i.
(IV) Tell your intuition for the change in the answers from part (2) to part (3). More speci?cally, tell when it was more likely that a red ball came from the ?rst urn (in other words, given you observed a red ball, what is the probability it came from the ?rst urn) and why this happened.
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