The odds against a certain event are 5 to 2, and the odds in favor of another event independent of the former are 6 to 5. Find the chance that one at least of the events will happen.

Explanation

Assme two events be E_{1} and E_{2}


Given: Odd against favour of one are `5: 2`


`Rightarrow` odds in favour are `2: 5`


`Rightarrow `Probability of happenig of one `=P(E)_{1}=frac{2}{7}`


`Rightarrow `probabiility of not happening one `=P(overlineE)_(1)=1-frac{2}{7}=frac{5}{7}`


Given: odds in favour of two are `6: 5`


`Rightarrow P(E)_{2}=frac{6}{11}`


`Rightarrow P(overlineE)_(2)=1-frac{6}{11}=frac{5}{11}`


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