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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?

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.

Algebra

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