1. Batman and Spiderman's Probability Problems

2. Batman and Spiderman have lots of people who want to get rid of them, but some are more dangerous than others, so he has to pick and choose who to battle against to keep the public as safe as possible. Each makes their decision independently, meaning that a previous fight doesn't affect who he chooses to fight next. Batman gives each choice a fractional or decimal value that adds up to 1, whereas Spiderman uses a similar system but with decimals.

3. Batman's Choices

4. Batman's Choice 1: Batman Joker Bane Riddler Penguin Riddler Penguin 1313 2323 1414 3434 1414 3434 Fight 1 - Bane or Joker (Joker is twice as dangerous as Bane) Fight 2 - Riddler or Penguin (Penguin is 3 times as dangerous as Riddler)

5. Batman Joker Bane Riddler Penguin Riddler Penguin 1313 2323 1414 3434 1414 3434 Batman's Choice 1: What is the probability that Batman will have the following battles: ·Joker then Penguin? ·Bane then Penguin?

6. Batman's Choice 2: Batman Harley Quinn Catwoman White Rabbit Fright 3535 2525 1515 4545 1515 4545 White Rabbit Fright Fight 1 - Catwoman or Harley Quinn Fight 2 - Riddler or Penguin

7. Batman's Choice 2: What is the probability that Batman will have the following battles: ·Catwoman then Fright? ·Harley Quinn then White Rabbit? Batman Harley Quinn Catwoman White Rabbit Fright 3535 2525 1515 4545 1515 4545 White Rabbit Fright

8. Batman's Choice 3: Batman Professor Milo Dr Double X Dr Phosphorus Professor Pyg 1313 2323 4747 3737 4747 3737 Dr Phosphorus Professor Pyg Fight 1 - Dr Double X or Professor Milo Fight 2 - Dr Phosphorus or Professor Pyg

9. Batman's Choice 3: What is the probability that Batman will have the following battles: ·Professor Milo then Dr Phosphorus? ·The Professors? ·He must fight at least 1 Doctor? Batman Professor Milo Dr Double X Dr Phosphorus Professor Pyg 1313 2323 4747 3737 4747 3737 Dr Phosphorus Professor Pyg

10. Batman's Choice 4: Batman KG Beast David Cain Jezebel Jet Lynx 1616 2626 3535 2525 3535 2525 Killer Croc 3636 Jezebel Jet Lynx Jezebel Jet Lynx 3535 2525 Fight 1 - David Cain, Killer Croc or KG Beast Fight 2 - Jezebel Jet or Lynx

11. Batman's Choice 4: What is the probability that Batman will have the following battles: ·KG Beast then Jezebel Jet? ·Killer Croc then Lynx? ·He will not fight David Cain or Lynx? Batman KG Beast David Cain Jezebel Jet Lynx 1616 2626 3535 2525 3535 2525 Killer Croc 3636 Jezebel Jet Lynx Jezebel Jet Lynx 3535 2525

12. Spiderman's Choices

13. Spiderman's Choice 1: Spiderman Shriek Carnage Mind Blast Whiplash 0.7 0.3 0.4 0.6 Mind Blast Whiplash 0.4 0.6 Fight 1 - Carnage or Shriek Fight 2 - Mind Blast or Whiplash

14. Spiderman's Choice 1: What is the probability that Spiderman will have the following battles: ·Shriek then Mind Blast? ·Carnage then Whiplash? Spiderman Shriek Carnage Mind Blast Whiplash 0.7 0.3 0.4 0.6 Mind Blast Whiplash 0.4 0.6

15. Spiderman's Choice 2: Spiderman Grizzly Spot Gibbon Kangaroo 0.8 0.2 0.1 0.9 0.1 0.9 Gibbon Kangaroo Fight 1 - Spot or Grizzly Fight 2 - Gibbon or Kangaroo

16. Spiderman's Choice 2: What is the probability that Spiderman will have the following battles: ·Spot then Kangaroo? ·He will fight at least one villain whose name begins with G? Spiderman Grizzly Spot Gibbon Kangaroo 0.8 0.2 0.1 0.9 0.1 0.9 Gibbon Kangaroo

17. Spiderman's Choice 3: Spiderman Rhino Beetle Hydro Man Boomerang 0.35 0.65 0.55 0.45 0.55 0.45 Hydro Man Boomerang Fight 1 - Beetle or Rhino Fight 2 - Hydro Man or Boomerang

18. Spiderman's Choice 3: What is the probability that Spiderman will have the following battles: ·Rhino then Hydro Man? ·Have exactly one battle with a villain whose name begins with B? Spiderman Rhino Beetle Hydro Man Boomerang 0.35 0.65 0.55 0.45 0.55 0.45 Hydro Man Boomerang

19. Spiderman's Choice 4: Spiderman Sandman Dr Octopus Green Goblin Venom 0.75 0.25 0.6 0.24 0.6 0.24 0.16 Juggernaut 0.16 Green Goblin Venom Juggernaut Fight 1 - Dr Octopus or Sandman Fight 2 - Green Goblin, Juggernaut or Venom

20. Spiderman's Choice 4: What is the probability that Spiderman will have the following battles: ·Dr Octopus then Juggernaut? ·He will not fight Sandman or Venom? Spiderman Sandman Dr Octopus Green Goblin Venom 0.75 0.25 0.6 0.24 0.6 0.24 0.16 Juggernaut 0.16 Green Goblin Venom Juggernaut

21. The streets are now safe!