Solutions to Mad Cow Madness

Mad Cow Risk

First, we will estimate the risk of getting, hence dying from, a disease-inducing-serving of beef during the British "Mad Cow Epidemic". We will estimate this risk by using the ratio of the number of disease-inducing-servings of beef caused by the epidemic to the total number of beef servings produced by Britain during the epidemic.

Let us first determine our denominator. Using this data we find that the United Kingdom produces about (1000)(1000) tonnes of beef for consumption each year. Using a conversion table this is (1000)(1000)(.9842)(2240) pounds or rather about 2(10^9) pounds. Let us assume that a serving is about 1/2 a pound. Then the British beef industry produces about (2)(2)(10^9) servings of beef a year. This epidemic lasted at least five years. Hence their were at least (5)(2)(2)(10^9) servings of beef produced.

Now let us estimate our numerator. Recall, there were about 140 deaths attributed to diseased cow meat during the Mad Cow Epidemic in Britain. Hence of the 5(2)(2)(10^9) servings of beef, we will estimate about 140 were disease inducers.

From these estimates, the chance of a given serving of beef being a disease-inducing-serving is about 140/((5)(2)(2)(10^9))=70/(10^10), or rather a bit less than 100/(10^10) = 1/(10^8).

Discussion Topics:

1. Discuss the relevance of this computation to the current U.S. "Mad Cow Scare".

2. Discuss the assumptions we made in order to interpret our ratio as a chance.

3. Discuss the assumptions we made in order to estimate this ratio's numerator and this ratio's denominator.

4. Discuss whether or not it is reasonable to consider our estimate a worst case scenario.

Driving Risk

Second, we will estimate the risk associated to driving a mile. First choose our possibilities, namely all the miles driven. From this data we find there were 2.6 (10^12) miles driven in US in 2000. Now we need to estimate which of these miles ended in an occupant fatality. Using this data as well as the above, we find that there were (41,717-5,842) (or about 35000) occupant fatalities. ASSUMING that each fatality corresponds to some given mile, we have that our risk of being killed in a given mile is about (35000)/(2.6(10^12)) or very nearly 10^4/10^12 = 1/10^8.

Discussion Topics:

1. Discuss the assumptions we made in order to interpret such our ratio as a chance.

2. Discuss the assumptions we made in order to estimate this ratio's numerator and this ratio's denominator.

Jackpot Chance

This is well known that the odds of winning the Powerball jackpot are 1 in 1.2(10^8). In other words, the chance of winning the jackpot is about 1/10^8.

Discussion Topics:

1. Discuss how you could figure out this number yourself.