How do you find the probability of an event occurring given the odds of the event?

1 Answer

See below:


Let's say we're talking about the tossing of a coin. The odds in a coin toss are:

#1:1; "Heads":"Tails"#

This says that out of 2 flips of a coin, you'd expect 1 Heads and 1 Tails.

Now let's talk about the probability of getting heads in a coin flip.

We know that out of 2 coin flips, 1 should be heads, so we can write the probability as:

#P("heads in a coin flip")=1/2#

Let's do it again, this time with the odds on a particular horse in a race. If the odds are #5:1; "Win": "Lose"#, what's being said is that the calculated probability of the horse winning is #5/6# - out of 6 races, the horse is anticipated to win 5 of them.

And so we can say that odds can be converted into probability by adding the numbers within the odds and putting that into the denominator and then putting the sought after requirement (such as Heads or Win) into the numerator.