Question

Selections with Replacement When randomly selecting items, if successive selections are made with replacement of previously selected items, which of the five rules of this section apply: (1) fundamental couting rule; (2) factorial rule; (3) permutations rule (when all items are different); (4) permutations rule (when some items are identical to others); (5) combinations rule?

Name: Problem 4, Chapter 4: Elementary Statistics
Uploaded: 2021-11-28T01:44:48-08:00
Duration: 19 s
Channel: Trent Speier
Description: Selections with Replacement When randomly selecting items, if successive selections are made with replacement of previously selected items, which of the five rules of this section apply: (1) fundamental couting rule; (2) factorial rule; (3) permutations rule (when all items are different); (4) permutations rule (when some items are identical to others); (5) combinations rule?

   Selections with Replacement When randomly selecting items, if successive selections are made with replacement of previously selected items, which of the five rules of this section apply: (1) fundamental couting rule; (2) factorial rule; (3) permutations rule (when all items are different); (4) permutations rule (when some items are identical to others); (5) combinations rule?

Elementary Statistics

Mario F. Triola 12th Edition

Chapter 4, Problem 4

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Solved by Expert Trent Speier

11/28/2021

Step 1

Step 1: When we are randomly selecting items with replacement, it means that after each selection, the item is put back into the pool and could be selected again. Show more…

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Selections with Replacement When randomly selecting items, if successive selections are made with replacement of previously selected items, which of the five rules of this section apply: (1) fundamental couting rule; (2) factorial rule; (3) permutations rule (when all items are different); (4) permutations rule (when some items are identical to others); (5) combinations rule?

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Key Concepts

Fundamental Counting Rule

This rule, also known as the multiplication principle, states that if one event can occur in a ways and a subsequent event can occur independently in b ways, then the total number of outcomes is a × b. In the context of selections with replacement, each selection is independent because replacing the item resets the number of available choices, allowing the multiplication of the number of options for each independent selection.

Selections with Replacement

When selections are made with replacement, each draw is independent of the previous ones, as the total number of options remains constant after every selection. This concept is critical because it validates the use of the fundamental counting rule to calculate probabilities or counts, avoiding the need for more complex rules such as the factorial, permutations, or combinations rules which are typically used when selections are made without replacement.

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