Question

find the odds of an event occurring, given the probability ½

Answer 1

The odds of an event is the ratio of the probability of an event to the probability of its complement.

To find the odds of an event with probability of 1/2:

1. Find the probability of the complement:

The probability of the complement (-E) is equal to 1 less the probability of the even (E):

$\begin{gathered} P(-E)=1-P(E) \\ P(-E)=1-\frac{1}{2}=\frac{1}{2} \end{gathered}$

2. Find the odds:

$P(E)\colon P(-E)$

$\frac{1}{2}\colon\frac{1}{2}$

Or:

$1\colon1$Then, ther oddds of an event ocurring, given the provavility 1/2 are 1:1 (1 to 1)