Probabilities #1
Exercise 1: Probabilities - NewsFlash ... Bob beats Strider
Hiryu in game of dice!
- So, Bob managed to roll higher scores than Hiryu in a game of
dice.
Actually he beat him 10 times out of the 12 tries they had arranged for
this. Now Hiryu is pissed, but does he have sufficient evidence to
claim that cheating is at work? What are the chances that this outcome
has emerged due to chance alone?
Exercise 2: Probabilities - The World Series
- Consider that the 2019 World Series is played by two teams, the
spitty A-sox and the scratchy B-balls. This year both teams have an
even chance of winning W(A)=W(B)=0.5. These teams play a series of
games in a best of seven contest. The team that wins four games is
declared the winner of the world series. What are the respective
chances that the World Series is decided after 4, 5, 6 and 7 games?
Exercise 3: Marking crayfish
- Karen wants to individually mark crayfish
in the field
using little plastic tags that come in one of 3 different colors. One
tag
can be inserted in 3 different locations into the animal without
harming it and multiple locations may be used per animal. How many
different individual crayfish can be marked for a recapture study?
Exercise 4: Statistical Research Group (SRG)
The US has just entered WWII and you are fighting the battle in
the Statistical Research Group (SRG) working out how to better protect
your bombers. We are taking losses and the planes coming back are shot
up by the German Air defenses. The damage isn’t uniformly distributed
across the aircraft. There are, on average, more bullet holes in the
fuselage, not so many in the engines.
| Section of Plane |
Bullet holes/m2 |
Engine
|
1.11 |
Fuselage
|
1.73 |
Fuel system
|
1.55 |
| Rest of
plane |
1.8 |
Your job is to figure out where and how much to armor the planes to
give them a better chance. But armor makes the plane heavier, less
maneuverable, and use more fuel. Armoring the planes too much is a
problem; armoring them too little is a problem too. Which sections
would you selectively reinforce, and why?
Competences earned this week:
- review concepts using probabilities
last modified: 1/20/15