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# Bag I contains 3 black and 2 white balls,Bag II contains 2 black and 4 white balls.A bag and a ball is selected at random .Determine the probability of selecting a black ball.

Toolbox:
• Bag 1has 3 Black and 2 White
• Bag 2has 2 Black and 4 White
• $E_1$=First bag is chosen
• $E_2$=secound bag is chosen
• A=Black ball drawn
• P(A)=$P(E_1$)$P(A/E_1$)+$P(E_2$)$p(B/E_2$)
Probability of choosing Bag 1=Probability of choosing Bag 2
$P(E_1$)=$P(E_2$)=$\large\frac{1}{2}$
$P(A/E_1$)=P(getting a black ball if 1 bag is chosen)=$\large\frac{3}{5}$
$p(B/E_2$)=P(getting a black ball if 2bag is chosen)=$\large\frac{2}{6}$
P(A)=$\large\frac{1}{2}\times$$\large\frac{3}{5}$+$\large\frac{1}{2}\times$$\large\frac{2}{6}$
=$\large\frac{3}{10}$+$\large\frac{1}{6}$
=$\large\frac{7}{15}$

edited Jun 4, 2013