Answer:
The probability that at least one of the children get the disease from their mother is P=0.7125.
Step-by-step explanation:
This can be modeled as a binomial random variable.
The parameter p=0.34 is the probability of a child being infected, and is constant and independent of the other events.
The parameter n=3 is the number of children (sample size).
Then, we have to calculate the probabilty that at least one of the children get the disease from their mother. That is:
The probability of exactly k children being infected can be calculated as:
Then, the easiest way to calculate this probability is using the complement: the value of the probability is 1 (or 100%) less the probability that no children gets infected.