Probability & Odds Help

The probability of an event successfully occurring is the number of ways an event can successfully occur divided by the total number of possible outcomes which includes all successes and failures.

P(s) = s/(s+f)

The complement, or probability of an event failing to occur is the number of ways it will fail to occur divided by the total number of possible outcomes.

P(f) = f/(s+f)

If you add the probability of an event occuring and the probability of an event not occuring, you have all of the possibilities.

Example 1: If you flip a coin, what is the probability, it will come up heads?. A coin only has two possible outcomes, either heads or tails. There is only one head and only one tail. So the probability of a coin coming up heads is 1/2 (50%). The probability of it not coming up heads is 1/2 (50%). The sum being 1 (100%).

Example 2: If you roll six-sided die, what is the probability, that you will roll a two?. The die has six possible outcomes, only one of which is a two. Five of the possibilities are not a two. So the probability of a rolling a two is 1/6 (16⅔%). The probability of it not rolling a two is 5/6 (83⅓%). The sum again being 1 (100%).

Probability is always between 0 and 1, or 0% and 100%.

Probability of Success + Probability of Failure = 1, or 100%.

Odds are similar to probability but yet very different. Odds can be greater than one. The odds of success are the number of ways an event can successfully occur divided by the number of ways the event may fail to occur.

Look at example 1, above, heads had a 0.5 or 50% probability. Remember, if it wasn't heads, then it had to be tails. This means the odds are heads : tails = 1 : 1. It may sound better but it only translates to 50% probability.

Since odds = s/f and probability = s/(s+f), if you add the successes to the denominator, you have probability.

Converting 3 to 1 odds means you have to add the 3 success to the denominator, making the probability 3/(3+1) = 3/4 = 75%.

Converting probability to odds may be a little more difficult since it is usually in decimal or percent form. If you have 75% probability of success, then you must have a 25% probability of failure. These are your odds, i.e. odds = 75% : 25% = 3 to 1.