Suppose that a disease is inherited via a dominant mode of inheritance and that

Question

Suppose that a disease is inherited via a dominant mode of inheritance and that only one of the two parents is affected with the disease. The implications of this mode of inheritance are that the probability is 0.3 that any particular offspring will get the disease, and is 0.15 that all the offspring will get the disease. For a family with two children, treat two affected children as two different events such that O = {older child is affected}, Y = {younger child is affected}.

a. Are the events O = {older child is affected} and Y = {younger child is affected} independent? Why or why not?

b. What is the probability that at least one sibling is affected?

c. Given the younger child is affected, what is the probability that the older child is affected?

Explanation / Answer

P( older child affected ) = 0.3 because the probability is 0.3 that any particular offspring will get the disease.

Similarly P( younger child is affected ) = 0.3

P( both affected ) = 0.15 because there is a probability of 0.15 that all the offspring will get the disease

Now computing: P( older child affected ) P( younger child is affected ) = 0.32 = 0.09

Therefore P( older child affected ) P( younger child is affected ) is not equal to P( both affected )

Therefore the 2 events are not independent.

b) Probability that at least one of the 2 get affected is computed as:

= 1 - Probability that none is affected

= 1 - (1-0.3)2

= 0.51

Therfore 0.51 is the required probability here.

c) Given that the younger child is affected, probability that the older is affected is computed using the bayes theorem as:

P( older affected | younger affected ) = P( both affected ) / P( younger affected ) = 0.15 / 0.3 = 0.5

Therefore 0.5 is the required probability here.

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