# What is the probability that the other brochure in the envelope is a Maui brochure in the following case:A statistics professor and his wife are planning to take a 2-week vacation in Hawaii, but...

What is the probability that the other brochure in the envelope is a Maui brochure in the following case:

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 on Maui, or 2 weeks on 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 brochure) and observes that it is a Maui brochure.

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### 1 Answer

The professor and his wife insert two brochures of Maui in one envelope, two brochures of Oahu in another envelope and one brochure each of Maui and Oahu in the third envelope.

When the professor's wife makes a random selection, he removes one brochure and notices that it is a Maui brochure. The professor could have done this either if his wife chose the envelope having both brochures from Maui or if there is one brochure of each of the places in that envelope. In the latter case, the other other brochure is not a Maui brochure. The probability of this is (1/3). In the former case, the other brochure is also from Maui. The probability of this is also (1/3).

As there is an equal probability of the envelope being the one with two brochures from Maui or the one with one brochure from both the places. This gives the probability that the other brochure in the envelope is from Maui as 0.5