Question

A bag contains 9 marbles: 2 are green, 3 are red, and 4 are blue. Raina chooses a marble at random, and without putting it back, chooses another one at random. What is the probability that both marbles she chooses are red? Write your answel as a fraction in simplest form.
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Answer 1

Answer:   1/12

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Explanation:

There are 3 red out of 9 total

The probability of picking red at random is 3/9 = 1/3

If the first marble is not put back, then the chances of picking red again are now 2/8 = 1/4

Notice how I subtracted 1 from the numerator and denominator of 3/9 to get to 2/8. This is because the red count and the total count both go down by 1 each.

Now multiply the fractions mentioned:

(3/9)*(2/8) = (1/3)*(1/4) = (1*1)/(3*4) = 1/12

If you did this trial 12 times, then you should expect to get two reds about once. That's one way to interpret the probability of 1/12.

Side note: 1/12 = 0.0833 = 8.33% approximately