A bag contains 3 blue balls, 4 red balls and 5 vellow balls. Three balls are randomly drawn one by one withoutreplacement. (a) Given that the first two balls are blue, find the probability that the third ball is blue. (b)Given that the first ball is blue and the second ball is yellow, find the probability that the third ball is red.c.Given that the first ball is red and the second ball is yellow, find the probability that the third ball is yellow
Question
A bag contains 3 blue balls, 4 red balls and 5 vellow balls. Three balls are randomly drawn one by one withoutreplacement. (a) Given that the first two balls are blue, find the probability that the third ball is blue. (b)Given that the first ball is blue and the second ball is yellow, find the probability that the third ball is red.c.Given that the first ball is red and the second ball is yellow, find the probability that the third ball is yellow
Solution
(a) Given that the first two balls are blue, the number of blue balls left in the bag is 1 (since we started with 3 blue balls). The total number of balls left in the bag is 10 (since we started with 12 balls and have drawn 2). Therefore, the probability that the third ball is blue is 1/10.
(b) Given that the first ball is blue and the second ball is yellow, the number of red balls left in the bag is 4 (since we haven't drawn any red balls yet). The total number of balls left in the bag is 9 (since we started with 12 balls and have drawn 2). Therefore, the probability that the third ball is red is 4/9.
(c) Given that the first ball is red and the second ball is yellow, the number of yellow balls left in the bag is 4 (since we started with 5 yellow balls and have drawn 1). The total number of balls left in the bag is 9 (since we started with 12 balls and have drawn 2). Therefore, the probability that the third ball is yellow is 4/9.
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