Question

John and Martha are contemplating having children, but John’s brother has galactosemia (an autosomal recessive disease) and Martha’s great-grandmother also had galactosemia. Martha has a sister who has three children, none of whom have galactosemia. What is the probability that John and Martha’s first child will have galactosemia

Answer 1

`Probability=(1)/(24)`

Explanation:

As the question states,

John's brother has Galactosemia which states that his parents were both the carriers.

Therefore, the chances for the John to have the disease is = 2/3

Now,

Martha's great-grandmother also had the disease that means her children definitely carried the disease means probability of 1.

Now, one of those children married with a person.

So,

Probability for the child to have disease will be = 1/2

Now, again the child's child (Martha) probability for having the disease is = 1/2.

Therefore,

The total probability for Martha's first child to be diagnosed with Galactosemia will be,

`Probability=(2)/(3)* (1)/(2)* (1)/(2)* (1)/(4)\\Probability=(1)/(24)`

(Here, we assumed that the child has the disease therefore, the probability was taken to be = 1/4.)

Hence, the probability for the first child to have Galactosemia is
`(1)/(24)`