1 / 10

120 likes | 429 Vues

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:

Télécharger la présentation
## Games of probability

**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.
Content is provided to you AS IS for your information and personal use only.
Download presentation by click this link.
While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

**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**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**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**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**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!**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**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!**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.

More Related