An urn has 3 blue balls 4 red balls. 3 balls are drawn without replacement. find the probability of drawing 2 blue and 1 red given at least 1 blue is drawn
+23245 The possibilities that contain at least one blue ball are:
blue - blue - blue (3/7) x (2/6) x (1/5) = 1/35
blue - blue - red (3/7) x (2/6) x (4/5) = 4/35
blue - red - blue (3/7) x (4/6) x (2/5) = 4/35
red - blue - blue (4/7) x (3/6) x (2/5) = 4/35
blue - red - red (3/7) x (4/6) x (3/5) = 6/35
red - blue - red (4/7) x (3/6) x (3/5) = 6/35
red - red - blue (4/7) x (3/6) x (3/5) = 6/35
1) The sum of all the probabilities that have exactely two blue balls is: 12/35.
2) The sum of all the probabilities that have at least one blue ball is: 31/35.
Dividing the result of 1) by the result of 2) gives: (12/35) / (31/35) = 12/31.
