# Thread: Probability of an event

1. ## Probability of an event

Probability of an event E if the odds in favor of E are as shown below,

a)2 to 15

Thanks so much.

2. ## Odds and probability

Hello ambergarrett955
Originally Posted by ambergarrett955

Probability of an event E if the odds in favor of E are as shown below,

a)2 to 15

Thanks so much.
If the odds in favour of E are 2 to 15, then in the long run we can expect E to happen 2 times for every 15 times it doesn't happen. In other words, for every 17 trials we can expect E to occur 2 times.

So the probability of E is $\displaystyle \frac{2}{17}$.

If you want a formula, you can say that if the odds in favour of an event are $\displaystyle a$ to $\displaystyle b$, then the probability of the event is $\displaystyle \frac{a}{a+b}$.

Note also that if you're given the odds against something happening, you need to use the second number for the numerator of the fraction when you're working out the probability. For instance, if the odds are 10 to 1 against something happening, then the probability that it will happen is $\displaystyle \frac{1}{11}$, and the formula is:

If the odds against an event are $\displaystyle a$ to $\displaystyle b$, then the probability that the event occurs is $\displaystyle \frac{b}{a+b}$.