Question

Sickle cell anemia is a disease that results when a person has two copies of a certain recessive gene people with one copy of the gene are called carriers carriers do not have that the disease but can pass the gene on to their children or child born to parents who are both carriers has a probability of 0.25 and half of having sickle cell anemia a medical study samples 18 children and families were both parents are carriers what is the probability that five or more of the children have sickle cell anemia what is the probability that fewer than three of the children have sickle cell anemia would it be unusual if all of the children have sickle cell anemia

Answer 1

1)

here this is binomial with parameter n=18 and p=0.25

probability that five or more of the children have sickle cell anemia :

P(X>=5)=1-P(X<=4)=

1-∑x=0x-1   (nCx)px(q)(n-x) =

0.4813

2)

probability that fewer than three of the children have sickle cell anemia :

P(X<3)=

∑x=02     (nCx)px(1−p)(n-x)    =

0.1353

3)

P( all of the children have sickle cell anemia ) =0.25¹⁸ =1.46*10^-11 ~0.0000

since probability of this happening is extremly rare, this would be highly unusual