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furcal201
03-02-2010, 11:12 AM
This question must be trickier than I thought:

A statistics professor and his wife are planning to take a 2-week vacation in Hawaii, but they can't decide whether to spend 1 week on each of the islands of Maui and Oahu, 2 weeks in Maui or 2 weeks in Oahu. Placing their faith in random chance, they insert two Maui brochures in one envelope, two Oahu brochures in a second envelope, and one brochure from each island in a third envelope. The professor's wife will select one envelope at random, and their vacation schedule will be based on the brochures of the islands so selected. After his wife randomly selects an envelope, the professor removes one brochure from the envelope (without looking at the second) and observes that it is a Maui brochure. What is the probability that the other brochure in the envelope is a Maui brochure?

I did...P(M twice)=.25, P(M)=.5, therefore P(M given M)=.5
from the formula P(A and B)=P(A)*P(B given A)

However, what I did isn't right. Thanks for the help in advance, Mike

Martingale
03-02-2010, 02:35 PM
This question must be trickier than I thought:

A statistics professor and his wife are planning to take a 2-week vacation in Hawaii, but they can't decide whether to spend 1 week on each of the islands of Maui and Oahu, 2 weeks in Maui or 2 weeks in Oahu. Placing their faith in random chance, they insert two Maui brochures in one envelope, two Oahu brochures in a second envelope, and one brochure from each island in a third envelope. The professor's wife will select one envelope at random, and their vacation schedule will be based on the brochures of the islands so selected. After his wife randomly selects an envelope, the professor removes one brochure from the envelope (without looking at the second) and observes that it is a Maui brochure. What is the probability that the other brochure in the envelope is a Maui brochure?

I did...P(M twice)=.25, P(M)=.5, therefore P(M given M)=.5
from the formula P(A and B)=P(A)*P(B given A)

However, what I did isn't right. Thanks for the help in advance, Mike

http://latex.codecogs.com/gif.latex?P(M_2|M_1)=\frac{P(M_2,M_1)}{P(M_1)}=\frac{P(M_2,M_1)}{P(M_1,O_2)+P(M_1,M_2)}=\frac{\frac{1}{3}}{\frac{1}{6}+\frac{1}{3}}=\frac{2}{3}