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Question Number 131509 by snipers237 last updated on 05/Feb/21

Let a,b,c  be  no null integers. A ballot box contains  “a” black bowls and “b”white bowls.  After a print we put the bowl back in the ballot box with “c” another bowls of the same color.  Prove that the probability to extract a green bowl at any   print is always  p = (a/(a+b))

$${Let}\:{a},{b},{c}\:\:{be}\:\:{no}\:{null}\:{integers}.\:{A}\:{ballot}\:{box}\:{contains}\:\:``{a}''\:{black}\:{bowls}\:{and}\:``{b}''{white}\:{bowls}. \\ $$$${After}\:{a}\:{print}\:{we}\:{put}\:{the}\:{bowl}\:{back}\:{in}\:{the}\:{ballot}\:{box}\:{with}\:``{c}''\:{another}\:{bowls}\:{of}\:{the}\:{same}\:{color}. \\ $$$${Prove}\:{that}\:{the}\:{probability}\:{to}\:{extract}\:{a}\:{green}\:{bowl}\:{at}\:{any}\:\:\:{print}\:{is}\:{always} \\ $$$${p}\:=\:\frac{{a}}{{a}+{b}} \\ $$

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