SOLUTION: A jar contains a total of 20 marbles that are blue, green, or white. The number of white marbles is three more than the number of green marbles, and the number of blue marbles is o

Question 260304: A jar contains a total of 20 marbles that are blue, green, or white. The number of white marbles is three more than the number of green marbles, and the number of blue marbles is one more than twice the number of green marbles.
(a) There are ____ green marbles, ____ white marbles, and ____ blue marbles in the jar.
One marble is randomly selected, its color is noted, and it is returned to the jar. A second marble is randomly selected and its color is noted.
(b) The probability that both marbles selected are blue is_____ .
(c) The probability that the first marble selected is green and the second marble selected is white is_____ .
(d) The probability that one of the marbles selected is red is_____ .

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A jar contains a total of 20 marbles that are blue, green, or white. The number of white marbles is three more than the number of green marbles, and the number of blue marbles is one more than twice the number of green marbles.
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b + g + w = 20
w = g + 3
b = 2g + 1
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Substitute for b and w and solve for "g":
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2g+1 + g + g+3 = 20
4g + 4 = 20
4g = 16
g = 4 (# of green marbles)
---
w = g+3 = 7 (# of white)
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b = 2g+1 = 9 (# of blue)
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(a) There are _4___ green marbles, _7___ white marbles, and _9___ blue marbles in the jar.
One marble is randomly selected, its color is noted, and it is returned to the jar. A second marble is randomly selected and its color is noted.
(b) The probability that both marbles selected are blue is__(9/20)^2___ .
(c) The probability that the first marble selected is green and the second marble selected is white is__(4/20)(7/20)___ .
(d) The probability that one of the marbles selected is red is 0/20 = 0
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Cheers,
Stan H.
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