Probability and Odds are mathematics attempt to predict the future. The slightly more complicated types of calculations use either Combinations or Permutations. At this point, I need to add a disclaimer - for some reason, no one checked with me before coming up with these rules. Unlike the combination on your locker, a combination here means that the order does not matter. Rolling 6, 2, 5 is the same as rolling 2, 5, 6 when figuring odds using the rules for combinations. Permutations are used when the order does matter.
Now that I've explained this, we'll move on to simpler calculations as Combinations and Permutations are subjects better suited to Algebra II, than Algebra I. And, we are gearing this group of pages to Algebra 1 students. It is my intention to add information for Algebra II in the very near future.
In calculating the probability and odds of getting heads with the toss of a coin, or rolling a six with the throw of a die, you could actually toss the coin several times and see what happens. This is the experimental method of calculating odds. It's not very accurate. Just because the odds are against something, does not mean it won't happen. It means it will rarely happen.
I once bought a book on how to win at bingo. I bought it because bingo is an extremely random game and there really is no way to increase your odds. The book described how to pick your bingo cards, and I give them credit there may be better odds with some combinations of cards than others. But the rest of the book was just silly. It asked the player to keep track of what numbers were picked over time, and that would tell you what number was about to be picked. I guess the writer assumed that the bingo balls remembered when they were last picked and would think it was there turn? On a random event past performance is no indication of future performance. The odds of flipping heads, on a fair balanced coin, is 1 in 2. If you should flip heads 100 times in a row, the odds of flipping heads on the next flip, is still 1 in 2.
Anyway, using the experimental method you divide the number of times an event occurs by the number of times you tried (Occurrence/Trials) = odds.
The theoretical method of determining probability and odds is much much more accurate (if it's done correctly). here we divide the number of ways the event can occur by the total number of equally likely outcomes (Can Occur)/(Total Outcomes). So, if you are rolling a fair die, there are 6 equally likely outcomes, or the Total Outcomes = 6. If we want the odds of rolling an even number, there are three of those - 2, 4, and 6. So the odds of rolling an even number = 3/6 or 1 in 2. The odds of rolling a 3 = 1/6 or 1 in 6. One way to roll a three out of six equally probable other possible numbers.
XVII.. Square Root Functions
XVIII. Absolute Value Functions