On average there are about 17 fatalities due to airplane acc

On average there are about 1.7 fatalities due to airplane accidents for every 100 million miles own. On average there are about 1.4 fatalities due to car accidents for every 100 million miles driven. Assume that you will live an additional 60 years.

(a) Assuming that you average 5 trips per year, each which is 2000 miles each way (for a total of 20,000 miles per year). What is the probability that you die in a plane crash.

(b) Assuming the you average 10 miles per day, 365 days per year. What is the probability that you die in a car crash. (c) What phenomenon does this problem highlight, and why?

(d) How would the availability heuristic aect you judgment if you just saw on the news that a commercial ight got in a crash and everyone died?

Solution

On average there are about 1.7 fatalities due to airplane accidents for every 100 million miles own

It means , for 1 million miles flown, the probabilty of fatalities due to airplane accidents =1.7/100=0.017

On average there are about 1.4 fatalities due to car accidents for every 100 million miles driven.

It means , for 1 million miles driven, the probabilty of fatalities due to car accidents=1.4/100=0.014

a) Assuming that you average 5 trips per year, each which is 2000 miles each way (for a total of 20,000 miles per year).

Means you travel 2000*5=10000 miles by each way (by car and by plane) in a year .

first we convert miles in to million miles, so 10000 miles= 10000/1000000=1/100 million miles

So the probability that you die in a plane crash.= 1/100* 0.017=0.00017

b) Assuming the you average 10 miles per day, 365 days per year. What is the probability that you die in a car crash.

In ayear you travel 365*10 =3650 miles

the probability that you die in a car accident= 3650/1000000*0.014=0.00005

(c) What phenomenon does this problem highlight, and why?

This phenomenon is about deaths due to car accident and plane crash. The probabilites of each event is very small.

Hence this phenomenon is ver rare. This kind of phenomenon follws poisson distribution.