Question

A human gene carries a certain disease from the mother to the child with a probability rate of 34%. That is, there is a 34% chance that the child becomes infected with the disease. Suppose a female carrier of the gene has three children. Assume that the infections of the three children are independent of one another. Find the probability that at least one of the children get the disease from their mother.

Answer the following questions:

State the complement of the event "At least one of the children get the disease from their mother".
Find the probability of the complement. Round your answer to four decimals
Find the probability that at least one of the children get the disease from their mother.

Answer 1

The probability that at least one of the children get the disease from their mother is 0.7125.

Explanation:

We are given that a human gene carries a certain disease from the mother to the child with a probability rate of 34%.

Suppose a female carrier of the gene has three children. Assume that the infections of the three children are independent of one another.

Let Probability that children get the disease from their mother = P(A) = 0.34

SO, Complement of the event "At least one of the children get the disease from their mother"= P(A') = 1 - P(A)

where A' = event that children do not get the disease from mother.

So, P(A') = 1 - P(A) = 1 - 0.34 = 0.66

Now, probability that at least one of the children get the disease from their mother = 1 - Probability that none of the three children get disease from their mother

= 1 - P(X = 0)

= 1 - (0.66
`*` 0.66
`*` 0.66)

= 1 - 0.2875 = 0.7125