Odds For and Against

Hello everybody!
So today is a Friday and we don't have school today! Hurray! And then we have Easter weekend off next week so that's 3 short weeks in a row! Yay!
In case you haven't noticed, I'm quite excited about that.
And I'm also excited because my birthday is on Monday! I like my birthday! Because I get cake!

Well. That was interesting. Now I will talk about school. Like I'm supposed to.

In Math class we have our unit test on Thursday about probability. Last week I talked about Theoretical and Experimental probabilities, and Eric talked about Tree Diagrams so I'm going to talk about odds for and against an event.

So, let's say you are flipping a coin 3 times, and you want to find out the odds for getting two heads and one tails, in any order.
First, you would draw a tree diagram and list out the possible outcomes. I will skip the tree diagram part, because I would have to do that in Paint and then attach it and quite frankly I'm too lazy to do that.
Anyways, the possible outcomes are:
HHH
HHT
HTH
HTT
THH
THT
TTH
TTT
The ones in red are the favourable outcomes (two heads, one tails).

Now, odds are expressed in a part to part ratio in lowest terms.
Here is the formula.
Odds For = favourable outcomes : total outcomes - favourable
Then, we substitute in the numbers.
Odds For = 3 : 8 - 3
Odds For = 3 : 5
And we would take down to lowest terms if it was possible, but it isn't in this case.

Now we can do odds against getting more than one tail.
Here are the possible outcomes again:
HHH
HHT
HTH
HTT
THH
THT
TTH
TTT
The favourable ones are in green (more than one tail).

Here is the formula.
Odds Against = total - favourable : favourable ( <-- you will notice that it is the reverse of Odds For)
Now, we substitute in.
Odds Against = 8 - 4 : 4
Odds Against = 4 : 4
And then take it to lowest terms.
Odds Against = 1 : 1

So, that is how we figure out odds for and against an event.

Until next week,
-K