In the most recent expedition to Mars Elon Musk found an alien population of 500

Question

In the most recent expedition to Mars Elon Musk found an alien population of 500 individuals. With their consent, Musk decided to map their genes in order to further understand them. Three main genes stood out to the scientist. The first gene (Gene A) coded for skin color, which varied between green, blue, yellow and purple. The second gene (Gene B) coded for the number of eyes in the organism, which varied between 2, 3 or 4. Finally, the third gene (Gene C) coded for hair, or lack of hair. The frequencies of the alleles are described below. Frequency 332564 111239 261979 294218 Gene A Codes For: Green Skin Blue Skin Yellow Skin Purple Skin Gene B ET EH EF Frequency 563249 212187 224564 Codes For: 2 Eyes 3 Eyes 4 Eyes Gene C Frequency 004328 995672 Codes For: Bald Very Hairy What is the probability that (out of a random sample) you pick out an alien with the following genotype: (G Go( EE HH')?

Explanation / Answer

We are calculating empirical probability here as we are calculating probability of genotype of an already exsiting individual of a population.

No of aliens (GGGG) = 0.3325642×500 = 55

Probability = 55/500

No of EHEH aliens = 0.2121872×500 = 23

Probability = 23/500

No of HHHH aliens = 0.9956722×500 = 495

Probability = 495/500

Probability of given genotype = 55/500×23/500×495/500 =

626175/125000000 = 0.0050094

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