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# Probability problem watch

1. I got this probability question as homework, but I got very confused as I didn't know if I should calculate the balls in the 2 boxes as whole or if I should calculate the probability of the first box then add the probability of the second.
Any help is appreciated.
Thanks.

Here is the question:
There are 2 boxes, box A contains 20 white balls and 20 black balls, box B contains 10 white balls and 5 black balls. A box is chosen at random then a ball is taken at random from the chosen box, what is the probability that the ball is white?
First I thought, it should be the probability of box A + the probability of box B;
20/40 + 10/15 = 7/6
but then I thought it doesn't really make sense to me as this tells that I will always get a white ball?!
So I thought, I could do the probability of the whole lot;
30/55 = 6/11
this answer seems more reasonable, but then I was confused, as there are 2 boxes, so that the chances of a white ball being taken out of each ball should be different?
2. (Original post by Sapphireluna)
I got this probability question as homework, but I got very confused as I didn't know if I should calculate the balls in the 2 boxes as whole or if I should calculate the probability of the first box then add the probability of the second.
Any help is appreciated.
Thanks.

Here is the question:
There are 2 boxes, box A contains 20 white balls and 20 black balls, box B contains 10 white balls and 5 black balls. A box is chosen at random then a ball is taken at random from the chosen box, what is the probability that the ball is white?
First I thought, it should be the probability of box A + the probability of box B;
20/40 + 10/15 = 7/6
but then I thought it doesn't really make sense to me as this tells that I will always get a white ball?!
So I thought, I could do the probability of the whole lot;
30/55 = 6/11
this answer seems more reasonable, but then I was confused, as there are 2 boxes, so that the chances of a white ball being taken out of each ball should be different?
Do you know about tree diagrams for doing probability questions? In this case, you have a tree with two branching points: the first involves the choice of box A or box B; the second involves the choice of a white ball or a black ball. The probabilities along each branch multiply to get to the probability of an end node (e.g. a white ball from Box A); you then need to sum the probabilities of the appropriate end nodes.
3. Got it!
Thanks!

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