The HIV disease can be produced by three viruses (A, B, C). For mice, the probability of developi...
The HIV disease can be produced by three viruses (A, B, C). For mice, the probability of developing the disease if infected with the virus A is 1/3, with virus B is 2/3 and virus C is 1/7.
a) if a researcher inoculates a mouse with one of the viruses at random, what is the probability that the mouse develops the disease?
b) If a mouse is inoculated and develops the HIV disease, what is the probability that it was inoculated with virus C?
Homework Answers
a) P(the mouse develops the disease) = P(virus A and disease) + P(virus B and disease) + P(virus C and disease)
= (1/3 x 1/3) + (1/3 x 2/3) + (1/3 x 1/7)
= 0.38095
b) Bayes' Theorem: P(A | B) = P(A & B)/P(B)
P(virus C | the mouse develops the disease) = P(virus C and disease) / P(the mouse develops the disease)
= (1/3 x 1/7)/0.38095
= 0.125
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