Odds against an Event

Odds against an Event is the ratio of "Number of UnFavourable Choices (Failures)" to "Number of Favorable Choices (Successes)". ⇒ Odds against an Event = Number of UnFavourable Choices : Number of Favorable Choices (Or) Number of Failures : Number of Successes = mc : m (Or) = (n − m) : m

Finding Odds using Probability

• Odds in Favour/Favor of an Event 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 (Or) = m : (n − m) = m m + mc : mc m + mc = m m + (n − m) : (n − m) m + (n − m) = m n : mc n = m n : (n − m) n = P(Event) : P(Eventc) ⇒ Odds in Favour/Favor of an Event "A" = P(A) : P(Ac) • Odds against an Event Odds against an Event = Number of UnFavourable/UnFavorable Choices : Number of Favourable/Favorable Choices (Or) Number of Failures : Number of Successes = mc : m (Or) = (n − m) : m = mc m + mc : m m + mc (n − m) m + (n − m) : m m + (n − m) = mc n : m n (n − m) n : m n = P(Eventc) : P(Event) ⇒ Odds against an Event "H" = P(Hc) : P(H)

Finding Probability using Odds in Favour/Favor

Let Odds in Favour/Favor of an Event "A" be x : y. • For Event A Odds in Favour of an Event = Number of Favourable/Favorable Choices : Number of Unfavorable/UnFavourable Choices (Or) Number of Successes : Number of Failures x : y = mA : mAc If "k" is the common factor between mA and mAc, mA = kx and mAc = ky. Total no. of possible choices = No. of Favourable/Favorable Choices + No. of Unfavourable/Unfavorable Choices (Or) No. of Successes + No. of Failures ⇒ n = mA + mAc = kx + ky = k (x + y) Probability of Occurrence of (Success for) Event "A" = No. of Favourable/Favorable Choices (Successes) Total No. of possible Choices ⇒ P(A) = mA n = kx k(x + y) = x x + y Probability of Non-Occurrence of (Failure for) Event "A" = No. of Unfavourable/Unfavorable Choices (Failures) Total No. of possible Choices ⇒ P(Ac) = mAc n = ky k(x + y) = y x + y Where, odds in favor/favour of an event is x : y, • P(Event) = x x + y • P(Eventc) = y x + y

Finding Probability using Odds against

Let Odds against an Event "H" be p : q. • For Event H Odds against an Event = Number of Unfavorable/UnFavourable Choices : Number of Favourable/Favorable Choices (Or) Number of Failures : Number of Successes p : q = mHc : mH If "a" is the common factor between mH and mHc, mH = aq and mHc = ap. Total no. of possible choices = No. of Favourable/Favorable Choices + No. of Unfavourable/Unfavorable Choices Number of Failures + Number of Successes ⇒ n = mH + mHc = aq + ap = a (q + p) = a (p + q) Probability of Occurrence of (Success for) Event "H" = No. of Favourable/Favorable Choices (Successes) Total No. of possible Choices ⇒ P(H) = mH n = aq a(p + q) = q p + q Probability of Non-Occurrence of (Failure for) Event "H" = No. of Unfavourable/Unfavorable Choices (Failures) Total No. of possible Choices ⇒ P(Hc) = mCH n = ap a(p + q) = p p + q Where, odds against an event is x : y, • P(Event) = y x + y • P(Eventc) = x x + y