Answer:
1.98% probability that at least 11 members are categorized as low risk participants in two of three communities
Step-by-step explanation:
To solve this question, we need to use two separate binomial trials.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
Probability of at least 11 members being categorized as low risk participants.
12 members in the sample, so
30% chance to be categorized as high risk participants. So 100-30 = 70% probability of being categorized as low risk participants. So
This probability is
What is the probability that at least 11 members are categorized as low risk participants in two of three communities?
For each community, 8.50% probability of at least 11 members being categorized as low risk. So
Three comunities, so
This probability is P(X = 2).
1.98% probability that at least 11 members are categorized as low risk participants in two of three communities