# SOLUTION: there are 3 boxes containing respectively 1 white, 2 red, 3 black balls; 2 white, 3 red, 1 black ball; 3 white, 1 red and 2 black balls. a box is chosen at random and from it two b

Algebra ->  Algebra  -> Probability-and-statistics -> SOLUTION: there are 3 boxes containing respectively 1 white, 2 red, 3 black balls; 2 white, 3 red, 1 black ball; 3 white, 1 red and 2 black balls. a box is chosen at random and from it two b      Log On

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 Click here to see ALL problems on Probability-and-statistics Question 585040: there are 3 boxes containing respectively 1 white, 2 red, 3 black balls; 2 white, 3 red, 1 black ball; 3 white, 1 red and 2 black balls. a box is chosen at random and from it two balls are drawn at random. the two balls are 1 red and 1 white. what is the probability that they come from (1) first box (11) second box (111) third box?Answer by Theo(3464)   (Show Source): You can put this solution on YOUR website!you can draw a table as shown below: ``` W R B box number 1 1 2 3 box number 2 2 3 1 box number 3 3 1 2 ``` you take a box at random and draw 2 balls. the 2 balls are 1 red and 1 white. the probability that the balls came from box number 1 is: 1/6 * 2/5 = 2/30 * 2 possible ways this can happen = 4/30 = 2/15 the probability that the balls came from box number 2 is: 2/6 * 3/5 = 6/30 * 2 possible ways this can happen = 12/30 = 6/15 the probability that the balls came from box number 3 is: 3/6 * 1/5 = 3/30 * 2 possible ways this can happen = 6/30 = 3/15 you can also look at this as the possible ways you can get each type ball out of the total possible ways you can get 2 balls out of 6. this would use the combination formula of nCx where n is the total number of selections and x is the number you want to draw from. using this type of analysis, you get: the probability that the balls came from box number 1 is: (1C1 * 2C1) / 6C2) = (1 * 2) / (15) = 2/15 the probability that the balls came from box number 2 is: (2C1 * 3C1) / (6C2) = (2 * 3) / (15) = 6/15 the probability that the balls came from box number 3 is: (3C1 * 1C1) / (6C2) = (3 * 1) / (15) = 3/15