SOLUTION: a box contains 12 balls of which 4 are green and 8 are red. if 7 balls are drawn from the box at random, one by one with replacement, find the probability that exactily 3 balls dra

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Question 759800: a box contains 12 balls of which 4 are green and 8 are red. if 7 balls are drawn from the box at random, one by one with replacement, find the probability that exactily 3 balls drawn are green.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
a box contains 12 balls of which 4 are green and 8 are red. if 7 balls are drawn from the box at random, one by one with replacement, find the probability that exactily 3 balls drawn are green.



First we will find the probability of drawing the 7 in this particular order:
GGGRRRR, where G = drawing a green ball and R = drawing a red ball.
That is,

%284%2F12%29%284%2F12%29%284%2F12%29%288%2F12%29%288%2F12%29%288%2F12%29%288%2F12%29%22%22=%22%22%284%2F12%29%5E3%288%2F12%29%5E4%22%22=%22%22%281%2F3%29%5E3%282%2F3%29%5E4%22%22=%22%22%281%2F3%5E3%29%282%5E4%2F3%5E4%29%22%22=%22%222%5E4%2F3%5E7%22%22=%22%2216%2F2187

But they do not have to be chosen in the particular order GGGBBBB.
For instance, the order BBGBGBG or GBGBGBB would do just as well.
So we must multiply the probability of the particular order GGGBBBB
by the number of all possible orders. That is the number of ways to
choose 3 of the 7 positions to draw the 3 green balls in or
C(7,3) = 35. (The other 4 positions will of course be red balls).

So the answer is 35%22%22%2A%22%2216%2F2187%22%22=%22%22560%2F2187


Edwin