There are three boxes. B1, B2, B3 The probability of selecting them is 0.2, 0.2 , 0.6 respectively. 


B1 contains 3 red balls and 7 green balls.
B2 contains 5 red balls and 5 green balls.
B3 contains 2 red balls and 8 green balls.


If we select a box and then a ball from the box what is the probability that the ball is of red color. 


If we select the a ball and it turns out to be of green color what is the probability that it comes from B3 ?



Porbability of selecting balls from boxes
Well, this looks more like someone trying to get their homework done, but for the first part:


$ p = 0.2 \* \frac{3}{3+7} + 0.2 \* \frac{5}{5+5} + 0.6 \* \frac{2}{2+8}$


$ p = 0.06 + 0.10 + 0.12 $


$ p = 0.28 $


Showed the work for you too.


So if the probability that a chosen ball is red is 28%, then the probability that a chosen ball is green is 72%.


So what is {probability that chosen ball came from B3 | chosen ball is green}? Look up conditional probability, look up bayesian, etc.


$ p\_g = 0.2 \* \frac{7}{3+7} + 0.2 \* \frac{5}{5+5} + 0.6 \* \frac{8}{2+8}$


$ p\_g = 0.14 + 0.10 + 0.48 $


$ p\_g = 0.72 $


{ $p\_g3$ | green ball} = (picked from box 3 and green) / (picked green)


= 0.48 / 0.72


= 2 /3


Please do your homework yourself.
Showed the work for you too.


