Question

In the movie ’Up In The Air’, George Clooney plays a character that accumulates ten million miles flying in the US domestic system. We want to estimate if it is realistic to accumulate this amount of miles without avoiding the risk of dying in a plane crash. Historical data shows that probability of dying in a plane crash is about 1 in a 45 million chance. Using that statistic:
1. How many flights could a traveler take on average before dying in a plane crash?
2. How many flights could a traveler take before the risk of death would be %50?
3. What is the probability of dying in an air crash if one takes enough domestic flights to accumulate ten million miles? Assume that average length of a domestic US flight is around 610 miles.

Answer 1

1.

p(plane crash) = 1/(45 million )

no. of flights on average before dying = 1 / P(plane crash)

= 1 / ( 1/(45 million ))

= 45 million flights

2.

risk = no. of flights * P(plane crash)

0.50 = (no. of flights) * 1/(45 million )

no. of flights = 0.50 / ( 1/(45 million ))

= 22.5 million flights

3.

no. of flights = miles / average length of a flight

= 10 million / 610 = 16393.4426

p(dying) = risk = no. of flights * P(plane crash)

= 16393.4426 * (1 / (45 million))

= 0.0003643

(please UPVOTE)