Question

Children inherit many traits from their parents. Some inherited traits are not desirable. For example, if both parents are carriers, there is a 25% chance any child will have sickle-cell disease. If we assume no identical twins in a family, and both individuals in a couple are carriers, what is the probability none of their four children has the disease

Answer 1

The probability that none of their four children has the disease = 0.316

Step-by-step explanation:

Step 1 :

The probability that the child will have the specified disease if both the parents are carriers = 25% = 0.25

So the probability that the child does not have the specified disease = 1 - 0.25 = 0.75

Step 2 :

There are four children. The probability that each child has the disease is independent of the condition of the other children

The probability of more than one independent events happening together can be obtained by multiplying  probability of individual events

So, the probability that none of their 4 children has the sickle cell disease  = $(0.75)^{4}$ = 0.316

Step 3 :

Answer :

The probability no children has the specified cell disease = 0.316