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.

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.

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?

Example #1 - Solution 13 favorable outcomes 52 total outcomes 39 unfavorable outcomes The probability of drawing a heart is 13/52 or 1/4. The odds of drawing a heart 13:39 or 1:3. *Odds will often be written in ratio form!

Today Mr. Gill teaches students how to gamble… Let’s start with roulette.

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?

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.

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 $90. However, the other 10 times I lose my ten dollars meaning I lose $100. I come out with a net loss of $10.

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.

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.

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.

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.

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.

Dice Rolling As you can see 7, is the most likely, while 2 and 12 are the least likely.

Games are designed around this… Believe it or not game designers know this and use these probabilities when making their games.