SOLUTION: We cannot get the correct answer to this probability question: A bag contains red & blue marbles. you pick 2 marbles at random without replacing the first one. The probability of d

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Question 99847: We cannot get the correct answer to this probability question: A bag contains red & blue marbles. you pick 2 marbles at random without replacing the first one. The probability of drawing a blue and then a red is 4/15. The probability that your second marble is red if your first is blue is 2/3. Find the probability the first marble is blue.
Found 2 solutions by edjones, stanbon:
Answer by edjones(8007) (Show Source):
You can put this solution on YOUR website!
Since the probability of a red ball is 2/3 after a blue one was picked 2/3 of the balls in the bag are red.
2/3,4/6,6/9,8/15
before the 1st ball was drawn the probability of drawing a red was
2/4,4/7,6/10,8/16
8/16*8/15=64//240=4/15 eureka!
so the probability that the 1st ball is blue = 8/16 or 1/2
Ed

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A bag contains red & blue marbles. you pick 2 marbles at random without replacing the first one. The probability of drawing a blue and then a red is 4/15. The probability that your second marble is red if your first is blue is 2/3. Find the probability the first marble is blue.
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P(red and blue) = P(red | blue}*P(b)
4/15 = (2/3)*P(b)
P(blue) = (4/15)*(3/2) = 2/5
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Cheers,
Stan H.