Question

Suppose that at the beginning of March, a new strain of flu, flu-A, emerges and begins to spread through U-College undergraduates.

The symptoms of Flu-A are like the common flu, flu-B, and other respiratory illnesses. It is thought that the infection rate of Flu-A will be similar to that of Flu-A at other colleges, but that the disease will be much less deadly. Flu-A is expected to infect about 20 out of every 1,000 undergraduate students per month for the rest of the semester, while the flu-B is expected to infect about 30 out of every 1,000 undergraduates per month for the rest of the semester.

Assume that this rate remains the same for each of the remaining months in the semester (March, April, and May). There are currently 6,800 U-College undergraduates on campus.

You may assume that infection with Flu-A is independent of infection with the flu-B.

1. You and your two roommates are concerned about becoming ill, either with Flu-A or with Flu-B. Calculate the probability that all of you will successfully avoid contracting either Flu-B or Flu-A over the next month (by the end of March).
2. Comment on two assumptions required to make the calculation in part 1 and explain whether they are reasonable.
3. Calculate the total expected number of Flu-A cases among U College undergraduates over the next three months.
4. If more than 150 cases of Flu-A are observed among the undergraduates during the next month, the College will go into shut-down mode and cancel class meetings. What is the probability the College goes into shut-down mode by the end of March?

Answer 1

The above problem can be regarded as a problem of bernoulli distribution with success if u contract the flu and failure otherwise. Let Xi ~ Bernoulli(p1); p1=probability of i^th roommate contracting flu-A per month; Thus E(X)=20/1000=p1. Similarly, Yi ~ Bernoulli(p2); p2=probability of i^th roommate contracting flu-B; Thus E(X)=30/1000=p2; i=1,2,3

Thus, assuming that the contraction of either flu to 1 roommate is independent to that of the other. (I.e X1,X2,X3 are independent bernouli trials. and Y1,Y2,Y3 are also independent bernoulli trials). Thus, and follow binomial distribution.

P(all roommates avoiding flu A and flu B by the end of month)=P(All roommates avoid flu A all roommates avoid flu B)

=P(all roommates avoid flu A).P(all roommates avoid flu B)..........assuming infection with Flu-A is independent of infection with the flu-B

= = 0.859

Assumptions are needed as without the assumption of independence of bernoulli trials, sum will not follow binomial distribution. and without assuming that flu A is independent of infection by flu B we will not be abe to calculate intersection probability.

• Total expected cases of flue A among students:

E(infection to one student per month)=0.02

E(infection to 6800 students over 3 months)=4080.

thus, 4080 students are expected to contract flu A over next 3 months