Warm Up – 5/7 - Wednesday
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Transcript of Warm Up – 5/7 - Wednesday
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Warm Up – 5/7 - Wednesday
• A single bag contains 4 red and 3 yellow discs. Two discs are pulled from the bag and not replaced.
A) Draw a tree diagram modeling the probability.B) Find the probability that both discs are yellow.C) Find the probability that both discs are the same color.
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Odds
• Odds are similar to probability. • The probability shows the number of
favorable outcomes divided by the number of total outcomes.
• The odds of an event are the number of favorable outcomes divided by the number of non-favorable outcomes.
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Example #1
• Mr. Gill draws a card from a standard deck of cards.
• What is the probability that the card is a heart?
• What are the odds that the card is a heart?
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Example #1 - Solution
• 13 favorable outcomes• 52 total outcomes• 39 unfavorable outcomes• The probability of drawing a heart is 13/52 or .• The odds of drawing a heart 13:39 or 1:3.
• *Odds will often be written in ratio form!
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Today Mr. Gill teaches students how to gamble…
• Let’s start with roulette.
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Roulette Bets
• There are plenty of bets we can make on roulette. Lets start with the simple Red vs. Black. Betting Red or Black pays 1:1.
• Let’s say we throw down $10 on Black. • What are the odds of landing on Black?
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Roulette Odds
• There are 18 red spaces and 18 black spaces. • However, there is also to 0 and the 00 spaces. • This means I have 18 favorable outcomes
versus 20 unfavorable outcomes. • My odds are 18:20 which reduces to 9:10. This
means for every 19 bets I place I will win 9 and lose 10.
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Roulette Odds
• Imagine I put $10 down on black 19 times. • This means 9 times I will double my money
and walk away with ten extra dollars each time. I have gained .
• However, the other 10 times I lose my ten dollars meaning I lose $100.
• I come out with a net loss of $10.
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Roulette Bets
• Alright so the Casino will walk away ahead on Red vs. Black. What about the column bet which pays out 2:1. So if I put down $10, I walk away with $20 extra dollars.
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Column Bet
• I have 12 favorable outcomes. • The two other columns have 24 unfavorable
outcomes. • But again, the 0 and 00 are not included in my
columns so that is 2 more unfavorable outcomes.
• My odds of winning are thus 12:26 which reduces to 6:13.
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Column Bet
• Again, If I made 19 bets, I would win 6 and lose 13.
• If I placed $10 dollars down each time I won, I walk away with $120 extra dollars.
• However, I lose my 13 times meaning I lose $130 dollars.
• Again, the Casino took $10 from me.
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Roulette Odds and Payouts
• The game is designed to take your money! All of the payouts are less than the odds of winning meaning the majority of the time, the house wins.
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Mr. Gill teaches students how to Gamble…
• How you gamble is… you don’t!
• Here is the deal, the house always wins. They have designed the games to work that way.
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Dice Rolling• As you can see 7, is the most likely, while 2
and 12 are the least likely.
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Games are designed around this…
• Believe it or not game designers know this and use these probabilities when making their games.