## 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:

1. review concepts using probabilities