Games of probability
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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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Games of probability

Games of probability

What are my chances?


Games of probability 1324532

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


Games of probability 1324532

  • Roll two dice.


Games of probability 1324532

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


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  • 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


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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


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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!


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  • 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


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  • 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!


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  • 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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