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Odds in Favour and Odds Against an Event

Category : JEE Main & Advanced

As a result of an experiment if \[''a''\] of the outcomes are favourable to an event E and \[''b''\] of the outcomes are against it, then we say that odds are a to b in favour of E or odds are b to a against E.



Thus odds in favour of an event E



\[=\frac{\text{Number of favourable cases}}{\text{Number of unfavourable cases}}=\frac{a}{b}=\frac{a/(a+b)}{b/(a+b)}=\frac{P(E)}{P(\bar{E})}\].



Similarly, odds against an event E



\[=\frac{\text{Number of unfavourable cases}}{\text{Number of favourable cases}}=\frac{b}{a}=\frac{P(\bar{E})}{P(E)}\].

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