# Likelihood

Consider a basket of 3 mangoes. We measure the sugar content.

The are of the following sugar content (g are grams unit) 13g, 14g, 15g.

There are two farms this time.

P Farm that produces mangoes which sugar content is a normal distribution with mean 13g and std of 2gram.

N Farm that produces mangoes which sugar content is a normal distribution with mean 15g and std of 1gram.

Answer the following questions. (you may ignore combinatoric factor)

1. Compute the likelihood of finding the three mangoes for P farm.

2. Compute the likelihood of finding the three mangoes for N farm.

3. If we have no clue. If you have no idea about the total yearly production of each farm so you assume that they both produce the same amount. Which farm do these mangoes are more likely to come from?

4. If N has monopoly? If N is secretly an heir to a Multi-National Mango Coporate which holds a virtual monopoly over mango market. They produces 10 Million mangoes a year. While P farm is an artisan organic fame that produces 100 mango a year. Will this change the answer to the previous question? (Give a justifying calculation)

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