Question

Vase 1 contains 2 white and 4 black balls and vase 2 contains 4 white and 4 black balls. If a ball is drawn at random from one of the two vases, what is a probability that it is a white ball

Answer 1

$\huge\underline\mathsf{SOLUTION:-}$

$\mathcal\textbf{Here, in this question, we have to find the probability for a white ball, which is drawn at random.}$

$\textbf{It is given that:--Vase 1 contains 2 white and 4 black balls and vase 2 contains 4 white and 4 black balls}$

$\star\huge{Case-1}$

$\mathbb\textbf{ a white ball is drawn from Vase 1 and put in Vase II. Then a ball is drawn from one of the two vases.So, the probability of being it black is:-}$

$\star\boxed{{2}/{7}×{4}/{9}=8/63}$

$\star\huge{Case-2}$

$\mathsf\underline{A\:black\:ball \:is \:drawn \:from\: Vase 1 \:and\: put\: in \:Vase II. \:Then \:a \:ball\: is \:drawn \:from\: Vase\: II. \:The\: probability\: of \:being\: it\: black\: is:-}$

$\huge\star\boxed{4/7×5/9=20/63}$

$\mathfrak{Hence,\: the\: required \:probability\: is:-}$

$\huge{20/63+8/63=28/63}$