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Games of probability

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:

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Games of probability

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  1. Games of probability What are my chances?

  2. 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

  3. Roll two dice.

  4. 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

  5. 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

  6. 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

  7. 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!

  8. 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

  9. 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!

  10. 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.

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