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antitative Literacy
Hannah thompson 03/20/25 8:55 PM
Question 2, 11.4.5
HW Score: 10%, 1 of 10 points
Part 1 of?
Pointar 0 of 1
Savo
If two states are selected at random from a group of 10 states, determine the number of possible outcomes if the group of states are selected with replacement or without replacement.
If the states are selected with replacement, there are possible outcomes.

Ask by Salazar Parry. in the United States
Mar 21,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

If the states are selected with replacement, there are 100 possible outcomes.

Solution

Step 1. Understanding the Problem
We have a total of states and we are selecting states with replacement. When selection is done with replacement, the same state may be chosen more than once.
Step 2. Determine the Number of Outcomes
Since the first state can be any one of the states, there are possible outcomes for the first selection. Because the state is replaced, there are again possible outcomes for the second selection.
Thus, the total number of possible outcomes is given by
Final Answer
If the states are selected with replacement, there are possible outcomes.

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Bonus Knowledge

When selecting two states with replacement from a group of 10 states, each selection allows for any of the 10 states to be chosen again, making it a scenario of multiplication. So, the calculation is . This means there are 100 possible outcomes when states are selected with replacement!
On the other hand, if the states are selected without replacement, the first state can be any of the 10, but the second must be different—only 9 choices remain. That means the calculation becomes . Hence, there are 90 possible outcomes when selecting without replacement. It’s interesting how the rules change the game!

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