Question

As of March 31, 2020, there are 113 confirmed cases of the current pandemic in

Kane County, Illinois, and 6 confirmed deaths.

2a. Using these statistics, estimate the probability of a randomly-selected confirmed case of the

virus in Kane County leading to death.

Your probability in 2a does not really apply to all people, but to get an idea of what that number

means, assume your answer to 2a applies to everyone who contracts the virus.

2b. If a family of four people contracts the virus, what is the probability that they all die?

2c. If a family of four people contracts the virus, what is the probability that at least one dies?

2d. Would it be unusual for an infected family of four to all survive the virus?

2e. A study by Pew research shows that 50-64 year olds have a median of 75 facebook friends. If all 75 of those people were infected, what is the probability that at least one dies?

Answer 1

As of March 31, 2020, there are 113 confirmed cases of the current pandemic in Kane County, Illinois, and 6 confirmed deaths.

2a. Using these statistics, estimate the probability of a randomly-selected confirmed case of the virus in Kane County leading to death.

the probability of a randomly-selected confirmed case of the virus in Kane County leading to death is

ans: the probability of a randomly-selected confirmed case of the virus in Kane County leading to death is 0.0531

Your probability in 2a does not really apply to all people, but to get an idea of what that number means, assume your answer to 2a applies to everyone who contracts the virus.

Let X be the number out of 4 in the family who die. We can say that X has a binomial distribution with parameters, number of trials (number of people in the family) n=4, success probability (  the probability of a randomly-selected confirmed case of the virus leading to death) p=0.0531

The probabiity that X=x people of this family of 4 die is

2b. If a family of four people contracts the virus, what is the probability that they all die?

the probability that they all die is

ans: If a family of four people contracts the virus, the probability that they all die is 0.0000 (rounded to 4 decimals)

2c. If a family of four people contracts the virus, what is the probability that at least one dies?

the probability that at least one dies is

ans: If a family of four people contracts the virus, the probability that at least one dies is 0.1961

2d. Would it be unusual for an infected family of four to all survive the virus?

the probability that none die is

The probability of an infected family of four to all survive the virus is 0.8039. This probability is greater than 0.05 and hence this event of an infected family of four to all survive the virus is not a rare event.

ans: No, it would not be unusual for an infected family of four to all survive the virus

2e. A study by Pew research shows that 50-64 year olds have a median of 75 facebook friends. If all 75 of those people were infected, what is the probability that at least one dies?

Let X be the number out of 75 infected, who die. We can say that X has a binomial distribution with parameters, number of trials (number of people infected) n=75, success probability (  the probability of a randomly-selected confirmed case of the virus leading to death) p=0.0531

The probabiity that X=x people die is

the probability that at least one dies is

ans: If all 75 of the Facebook friends were infected, the probability that at least one dies is 0.9833