MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Concept explainers

Counting Principles
In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of …
Question

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
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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! (n – r)!] = [n (n – 1) … (n – r + 1)] / r! ways.

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