Probability and Odds in Favor/Favour or Against an Event

Finding Odds in favor/favour using Probability

Odds in Favour of an Event = Number of favourable/favorable choices
: Number of Unfavorable/UnFavourable Choices
(Or) = Number of Successes : Number of Failures
= m : mc
=
m
m + mc
:
mc
m + mc
=
m
n
:
mc
n
= P(Event) : P(Eventc)

alternatively

Odds in Favour of an Event = Number of favourable/favorable choices
: Number of Unfavorable/UnFavourable Choices
(Or) = Number of Successes : Number of Failures
= m : (n - m)
=
m
m + (n - m)
:
(n - m)
m + (n - m)
=
m
n
:
(n - m)
n
= P(Event) : P(Eventc)

⇒ Odds in favour/favor of an Event "A" = P(A) : P(Ac)

Finding Odds against using Probability

Odds against an Event = Number of unfavourable/unfavorable choices
: Number of favorable/Favourable choices
(Or) = Number of Failures : Number of Successes
= mc : m
=
mc
m + mc
:
m
m + mc
=
mc
n
:
m
n
= P(Eventc) : P(Event)

alternatively

Odds against an Event = Number of unfavourable/unfavorable choices
: Number of favorable/Favourable choices
(Or) = Number of Failures : Number of Successes
= (n - m) : m
=
(n - m)
m + (n - m)
:
m
m + (n - m)
=
(n - m)
n
:
m
n
= P(Eventc) : P(Event)

⇒ Odds against an Event "A" = P(Ac) : P(A)

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