A bag contains 5 red marbles, 9 white marbles, and 5 blue marbles. You draw 3 marbles out at random, without replacement. What is the probability that all the marbles are red? The probability that all the marbles are red is    . What is the probability that exactly two of the marbles are red? The probability that exactly two of the marbles are red is    . What is the probability that none of the marbles are red? The probability of picking no red marbles is

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 7ECP: You draw one card at random from a standard deck of 52 playing cards. What is the probability that...
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A bag contains 5 red marbles, 9 white marbles, and 5 blue marbles. You draw 3 marbles out at random, without replacement. What is the probability that all the marbles are red?

The probability that all the marbles are red is    .

What is the probability that exactly two of the marbles are red?
The probability that exactly two of the marbles are red is    .

What is the probability that none of the marbles are red?
The probability of picking no red marbles is 

Expert Solution
Step 1

The formula for combination is nCrn! / [r! (n – r)!] = [n (n – 1) … (n – r + 1)]/r!.

Explanation:

Consider that r distinct items need to be selected from n items and the selection must be without replacement. The order of selection does not matter.

In such case, the combination formula can be applied.

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