Question

One genetic disease was tested positive in both parents of one family. It has been known that any child in this family has a 25% risk of inheriting this disease. A family has three children. The probability of this family having one child who inherited this genetic disease is:

Answer 1

One genetic disease was tested positive in both parents of one family. It has been known that any child in this family has a 25% risk of inheriting this disease. A family has three children.

Now we want to find the probability that this family having one child who inherited this genetic disease.

Let define a random variable X, X : random variable denoting the number of children who inherited this genetic disease.

Here given that, any child in this family has a 25% risk of inheriting this disease.

[ Note:- A discrete probability distribution binomial distribution is frequently used to model the number of successes in a sample. For this problem we assume that one children inherited this genetic disease means one success. So X~ bin(3,0.25) Probability muss function of X is given by, P(x) =   , for this problem if we put x=1 then we get the required probability. ]

=> Required probability is,

P(1) = = 3×0.25×0.5625 = 0.421875

Note (using concept):- if X~ bin(n,p) then, P(x) = ; where n= number of independent trials, p= success probability in one independent trial, x= number of success.