Problem 9 [20 Pts]

The article entitled "Why outbreaks like coronavirus spread exponentially, and how to flatten the curve"

(which can be found here) provides a good explanation about the statistics of a virus like the coronavirus.

Now, assume a sample of 1,000 people was obtained. Of those 1,000 people, 600 were considered young (under

the age of 60) and 400 were considered old (over the age of 60). If you are old, there is a 0.2 probability of

experiencing complications due to the illness. If you are young, there is a 0.05 probability of experiencing

complications.

(a)

(4 pts) Make a two-way frequency table showing this information (remember that a frequency table

shows the counts, not the probabilities).

(b)

(5 pts) Make a table that shows marginal and joint distributions (make sure to identify which distri-

bution is marginal and which is joint). Provide an interpretation of one of the marginal probabilities

and one of the joint probabilities.

(c)

(3 pts) Make a table that shows the conditional distribution (assume that we are conditioning on being

young or old). Provide an interpretation for one of the conditional probabilities.

(d)

(3 pts) What is the probability of not experiencing complications given that you are young? What

is the probability that you do not experience complications AND that you are young? Explain the

difference between these two probabilities?

(e)

(5 pts) Using Bayes' theorem, calculate the probability that someone is old given that they experienced

complications.

link to article https://www.washingtonpost.com/graphics/2020/world/corona-simulator/