Exercise Marbles.A. A bowl contains 7 red marbles, 11 white marbles and 12 blue

Question

Exercise Marbles.A. A bowl contains 7 red marbles, 11 white marbles and 12 blue marbles. From the bowl, five are selected at random. For the selection, assume all marbles are equally likely to be chosen. For each of the following, you may the answer using formulas with combinations, or as fractions. (Use "n C r " for ``combinations nchoose r ''.)

What is the chance that no red marble is selected?

What is the chance that exactly two red marbles are selected?

What is the chance that exactly two blue marbles, two white marbles and one red marble are selected?

What is the chance that only red and white marbles are selected?

Explanation / Answer

Total marbles = 7 + 11 + 12 = 30

A) P(no red marble) = 23C5 / 30C5 = 0.2361

B) P(2 red marbles) = 7C2 * 23C3 / 30C5 = 0.2610

C) probability = 12C2 * 11C2 * 7C1 / 30C5 = 0.1783

D) probability = 18C5 / 30C5 = 0.0601

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