A bag contains 10 red marbles, 7 white marbles, and 5 blue marbles. You draw 5 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    .

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.8: Probabilities Of Disjoint And Overlapping Events
Problem 2C
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A bag contains 10 red marbles, 7 white marbles, and 5 blue marbles. You draw 5 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

Introduction:

According to the combination rule, if r distinct items are to be chosen from n items without replacement, in such a way that the order of selection does not matter, then the selection can be made in (nCr) = n! / [r! (nr)!] = [n (n – 1) … (nr + 1)] / r! ways.

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