所選文字: 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 回答問題
Question
所選文字: 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 回答問題
Solution
(a) Given that the first two balls are blue, the probability that the third ball is blue:
Step 1: Calculate the total number of balls in the bag. There are 3 blue balls, 4 red balls, and 5 yellow balls, so there are 3 + 4 + 5 = 12 balls in total.
Step 2: The first two balls drawn are blue, so there is now 1 blue ball left and a total of 10 balls left in the bag.
Step 3: The probability that the third ball is blue is therefore 1/10.
(b) Given that the first ball is blue and the second ball is yellow, the probability that the third ball is red:
Step 1: After drawing a blue and a yellow ball, there are 2 blue balls, 4 red balls, and 4 yellow balls left, so there are 2 + 4 + 4 = 10 balls in total.
Step 2:
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