SOLUTION: A bag contains 3 red and 5 blue marbles. Two are drawn together from the bag. FInd the probability that
a) they are both blue
b) they are blue if it is know that one marble is b
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-> SOLUTION: A bag contains 3 red and 5 blue marbles. Two are drawn together from the bag. FInd the probability that
a) they are both blue
b) they are blue if it is know that one marble is b
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Question 1122439: A bag contains 3 red and 5 blue marbles. Two are drawn together from the bag. FInd the probability that
a) they are both blue
b) they are blue if it is know that one marble is blue Answer by math_helper(2461) (Show Source):
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a) P(blue and blue) = (5/8)*(4/7) = 20/56 = , or about 0.3571
b) P(blue | blue) = P(blue and blue) / P( at least one blue) = (20/56) / (50/56) = 20/50 = or 0.40.
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Here is the probability distribution for the four raw outcomes:
1. P(B and B) = 20/56
2. P(R and B) = 15/56
3. P(B and R) = 15/56
4. P(R and R) = 6/56
Part(b) is equivalent to asking "once you know you are in one of the cases 1...3, what is the probability you have case 1?" There are 20+15+15 = 50 possible outcomes in cases 1...3, and 20 of them are case 1.
