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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-th




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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