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

P {First event does not happen} `=(5)/(5+2)=5/7`
P{Second event does not happen} `=(5)/(5+6)=5/11`
`therefore` {Both th events fail to happen} `5/7xx5/11=25/77`
Therefore, the probability that at least one of the events will happen is
1- P(none of two happens) `=1-(25)/(77)=(52)/(77)`