probability

Question

Suppose an opaque jar contains 7 red marbles and 10 green marbles. The following exercise refers to the experiment of picking two marbles from the jar without replacing the first one.

What is the probability of getting a green marble and a red marble? (Enter your probability as a fraction. Hint: How is this exercise different from finding the probability of getting a green marble first and a red marble second?)

Answer 1

The answer requires the use of the hypergeometric distribution.

I will use the notation nCr for the binomial coefficient = n!/((n-r)*r!).

The answer then is 7C1 * 10C1/17C2.

This question asks only that the selected marbles are one red and one green, irrespective of order.