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-(1)/(2)=(1)/(2) \end{gathered}`

2. Find the odds:

`P(E)\colon P(-E)`

`(1)/(2)\colon(1)/(2)`

Or:

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