Question Number 168259 by peter frank last updated on 07/Apr/22
$$\mathrm{If}\:\mathrm{the}\:\mathrm{odds}\:\mathrm{in}\:\mathrm{favour}\:\mathrm{of}\:\mathrm{an}\:\mathrm{event} \\ $$$$\mathrm{be}\:\frac{\mathrm{1}}{\mathrm{3}}.\mathrm{Find}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{of}\: \\ $$$$\mathrm{an}\:\mathrm{occurrence}\:\mathrm{of}\:\mathrm{the}\:\mathrm{event}. \\ $$
Answered by som(math1967) last updated on 07/Apr/22
$${if}\:{the}\:{probability}\:{of}\:{occurance}\: \\ $$$${be}\:\frac{{m}}{{n}}\:{then}\:\frac{{m}}{{n}−{m}}\:{is}\:{odd}\:{in}\:{favour} \\ $$$${of}\:{the}\:{event}\: \\ $$$$\:\therefore\:\frac{{m}}{{n}−{m}}=\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\Rightarrow\mathrm{3}{m}={n}−{m} \\ $$$$\Rightarrow\mathrm{4}{m}={n} \\ $$$$\therefore\:\frac{{m}}{{n}}=\frac{\mathrm{1}}{\mathrm{4}} \\ $$
Commented by peter frank last updated on 07/Apr/22
$$\mathrm{thank}\:\mathrm{you} \\ $$