A batrachologist is studying genetic mutations in a population of tree frogs, sp

Question

A batrachologist is studying genetic mutations in a population of tree frogs, specifically three common mutations denoted A, B, and C. For each of the three mutations, the probability is .2 that a frog in the population has only that mutation (and not the other two). For any two of the three mutations, the probability is .05 that a frog has exactly these two mutations (but not the other one). The probability that a frog has all three genetic mutations, given that it has mutations A and B, is 2/3. What is the probability that a frog has none of the three genetic mutations, given that it does not have mutation C?

Explanation / Answer

Here,

P(A only) = P(B only) = P(C only) = 0.2

P(exactly 2 mutations) = 0.05

P(3 mutations|A n B) = 2/3 = P(3 mutations|at least 2 mutations)

Hence,

P(exactly 3 mutations) = 0.10

Hence,

P(at least 1 mutation) = 3*P(any 1) + 3*P(any 2) + P(exactly 3) = 3*0.2 + 3*0.05 + 0.10 = 0.85

Hence,

P(no mutation) = 1 - P(at least one mutation) = 0.15

Therefore,

P(no mutation C) = 1 - P(C) = 1 - (0.2+2*0.05+0.10) = 0.60

Hence,

P(no mutation|no mutation C) = 0.15/0.60 = 0.25 [ANSWER]

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