Question

1. In New Mexico, 15% of residents are covered by Medicaid. 10% of residents are covered by Medicare. 3% of residents are dual eligible and covered by both Medicare and Medicaid. Draw a Venn Diagram and then calculate the probability that a New Mexico resident selected at random will be covered by either Medicare or Medicaid.

2.  A binomial distribution describes a random variable, X, that has 4 possible outcomes. Outcome 1 has a probability of 25%, Outcome 2 has a probability of 15%, Outcome 3 has a probability of 20%. What is the probability of Outcome 4?

Answer 1

Solution:

1. We are given that 15% of residents are covered by Medicaid. 10% of residents are covered by Medicare. 3% of residents are covered by both Medicare and Medicaid.

Therefore, we have:

We have to find:

Using the additional rule of probability, we have:

   

  

2.  A binomial distribution describes a random variable, X, that has 4 possible outcomes. Outcome 1 has a probability of 25%, Outcome 2 has a probability of 15%, Outcome 3 has a probability of 20%. What is the probability of Outcome 4?

Answer: We know that the total probability is 100%.

Therefore, the probability of outcome 4 is: