# The probability of an event E not occurring is 0.4. What are the odds in favor of E occurring?

##### 2 Answers

#### Explanation:

An event must either occur (

Therefore the sum of the probabilities of an event occurring and an event not occurring must be equal to 100%

That is

Given that

This implies that

The odds in favour of

#### Explanation:

An **odds in favour** is a ratio of "how likely an event is to occur" to "how likely it is to NOT occur". This can be derived from

#"number of favourable outcomes"/"number of unfavourable outcomes"#

or

#"proability of event occuring"/"probability of event not occurring"#

and is usually expressed in colon notation as

Given

#"P"(E)=1-"P"(E^"C")#

#color(white)("P"(E))=1-0.4#

#color(white)("P"(E))=0.6#

which gives

#"odds"(E)="P"(E):"P"(E^"C")#

#color(white)("odds"(E))=0.6:0.4#

This can be scaled up by 5, so that both numbers in the odds are whole numbers:

#"odds"(E)=0.6xx5" ":" ""0.4xx5#

#color(white)("odds"(E))=3:2# .