games of probability
Download
Skip this Video
Download Presentation
Games of probability

Loading in 2 Seconds...

play fullscreen
1 / 10

Games of probability - PowerPoint PPT Presentation


  • 101 Views
  • Uploaded on

Games of probability. What are my chances?. Activity 1: Simple probability: . Roll a single die (6 faces). What is the probability of each number showing on top?. Assume the die is fair. Roll two dice. Activity 2: Independence of two trials: . Roll a die and toss a coin:

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Games of probability' - kaloosh


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
games of probability

Games of probability

What are my chances?

slide2
Activity 1: Simple probability:
  • Roll a single die (6 faces).
    • What is the probability of each number showing on top?

Assume the die is fair

slide4
Activity 2: Independence of two trials:
  • Roll a die and toss a coin:
    • What is the probability of getting a “3 and Tail” ?
  • Probability of getting a 3 on the die = 1/6.
  • Probability of getting a tail on the coin = 1/2
  • Since the outcomes of the coin toss and the die rolling are independent, the join probability of getting a 3 AND a tail is (1/6)*(1/2)=1/12
slide5
Assume the odds of getting the tail from the coin is 1/3, head is 2/3.
    • What is the probability of getting a “3 and Tail” now ?
  • What if the coin is not fair?

Answer: 1/6 * 1/3 = 1/18

slide6
Activity 3: Who is the winner?
  • Toss a coin. Each time it’s head, you win $1, each time it’s tail, you lose $1.
  • Roll two dice. Each time it’s 7, you win $4, otherwise you lose $1.
  • Roll two dice. Each time it’s 7, you win $5, otherwise you lose $1.
  • Roll two dice. Each time it’s 7, you win $6, otherwise you lose $1.

Even

Loser

Even

Winner

slide7
Activity 4: Don’t be fooled
  • 3 piles of cards. 2 cards in each pile:
    • Pile 1: ♥K and ♥K
    • Pile 2: ♥K and ♠K
    • Pile 3: ♠K and ♠K
  • We don’t know which pile is which. Randomly pick one card from one pile. If the card we pick is ♥K, what is the odds that the other card in the pile is also ♥K?
  • Let’s do an experiment!
slide8
Ways to pick ♥K :
    • if we happen to pick a card from pile 1: either card will do.
    • If we happen to pick a card from pile 2: only one card will do.
    • If we happen to pick a card from pile 3: no card will do.
  • Probability of picking ♥K :(1/3)*(1)+(1/3)*(1/2)+(1/3)*0=1/2
  • Probability of picking a pile which has two ♥K: 1/3
  • So, knowing one card is ♥K, the probability of the other one is also ♥K is (1/3)/(1/2)=2/3
slide9
Will you be a winner if you play this game?
    • Each time when ♠K is picked, no win, no lose.
    • Each time when ♥K is picked, you win $3 if the other card is ♠K.
    • Each time when ♥K is picked, you lose $2 if the other card is ♥K.

You win $3 when you win, you only lose $2 when you lose…. Do you think you can make money by playing on?

NO!

DON’T BE FOOLED!

slide10
Most of the gambling games are like this example – The odds are not in favor of the player.
  • Use the concept of probability can help you determine whether a decision is good or bad – such as making investments.
  • Don’t gamble – unless your math tells you that you can win.
ad