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Question
12 red marbles
8 blue marbles
one marble chosen at random and not replaced.  then a second marble is chosen at random.
a) what is the probability the two marbles are NOT the same color?
b) what is the probability that at least one marble is red?

Answer
There are a total of 12+8 = 20 marbles.
This means that 12/20 = 3/5 are red.
This also means that 8/20 = 2/5 are blue.
The probabilities are
both red: (3/5)(3/5) = 9/25;
1 blue, 1 red: (3/5)(2/5) + (2/5)(3/5) = 6/25 + 6/25 = 12/25; and
both blue: (2/5)(2/5) = 4/25.

As can be seen, the total is 9/25 + 12/25 + 4/25 = 25/25 = 1, so that's right.

a) If the two are not the same color, that is 1 blue and 1 red,
and the probability is 12/25.

b) The probability of at least one red is 1 red 1 blue or 2 reds.
That is 12/25 + 9/25 = 21/25.

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Scott A Wilson

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Any algebraic question you've got. That includes question that are linear, quadratic, exponential, etc.

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I have solved story problems, linear equations, parabolic equations. I have also solved some 3rd order equations and equations with multiple variables.

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Documents at Boeing in assistance on the manufacturiing floor.

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MS at math OSU in mathematics at OSU, 1986. BS at OSU in mathematical sciences (math, statistics, computer science), 1984.

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Both my BS and MS degrees were given with honors.

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