Question Number 76651 by john santu last updated on 29/Dec/19
$${if}\:{a}\:{and}\:{b}\:{two}\:{numbers}\:{do}\:{not}\:{have}\: \\ $$$${to}\:{be}\:{chosen}\:{randomly}\:{and}\:{with}\: \\ $$$${returns}\:{from}\:{the}\:{set}\:\left\{\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5}\right\}.\:{what}\: \\ $$$${probability}\:{that}\:\frac{{a}}{{b}}\:{is}\:{an}\:{integer}\:? \\ $$
Answered by benjo 1/2 santuyy last updated on 29/Dec/19
$${suppose}\:{that}\:{A}\:{is}\:{the}\:{occurence}\: \\ $$$${of}\:{a}/{b}\:{integer}\:.\: \\ $$$${now}\:{n}\left({A}\right)=\:\mathrm{10}\:{and}\:{n}\left({S}\right)\:=\:\mathrm{5}×\mathrm{5}\:=\:\mathrm{25} \\ $$$${hence}\:{P}\left({A}\right)\:=\:\mathrm{10}/\mathrm{25}\:=\:\mathrm{2}/\mathrm{5}.\: \\ $$
Commented by benjo 1/2 santuyy last updated on 30/Dec/19
$$\mathrm{1}/\mathrm{1},\:\mathrm{2}/\mathrm{1},\mathrm{3}/\mathrm{1},\mathrm{4}/\bar {\mathrm{1}},\mathrm{5}/\mathrm{1},\:\mathrm{4}/\mathrm{2},\:\mathrm{2}/\mathrm{2},\:\mathrm{3},\mathrm{3},\: \\ $$$$\mathrm{4}/\mathrm{4}\:{and}\:\mathrm{5}/\mathrm{5}\:{sir} \\ $$
Commented by mr W last updated on 30/Dec/19
$${how}\:{did}\:{you}\:{get}\:{n}\left({A}\right)=\mathrm{10}? \\ $$
Commented by benjo 1/2 santuyy last updated on 30/Dec/19
$$\mathrm{2}/\mathrm{4}\:{not}\:{intger}\:{sir} \\ $$
Commented by mr W last updated on 30/Dec/19
$${you}\:{are}\:{right}\:{if}\:{it}\:{is}\:{defined}\:{that} \\ $$$${a}\:{is}\:{the}\:{first}\:{and}\:{b}\:{is}\:{the}\:{second} \\ $$$${number}\:{drawn}. \\ $$
Commented by benjo 1/2 santuyy last updated on 30/Dec/19
$${yes}\:{sir}.\:{thanks}\:{you} \\ $$