Math Problem Statement
Solution
I see that you’ve uploaded an image related to matching events to their corresponding probabilities. Let's break down each part to help match the events with the correct probabilities.
The set of tiles contains 10 numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Here are the events described in the image:
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Draw a 4-tile sequence, without replacement, that doesn't contain a 5.
- Since the set of 10 tiles includes the number 5, you would need to draw 4 tiles from the 9 remaining tiles (since we exclude 5). This affects the probability calculation.
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Draw a 4-tile sequence, without replacement, where the 4th tile is 3.
- In this case, the last tile in the sequence must be a 3, and the first three tiles must be drawn from the remaining 9 tiles. This will adjust the total number of possible outcomes.
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Draw the three-tile sequence "2, 1, 4", when drawing without replacement.
- The specific sequence "2, 1, 4" has to be drawn in this order, which means there are fewer possible sequences than when no specific order is required.
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Draw two tiles, without replacement, such that the number on the second tile is greater than the number on the first.
- This requires calculating how many pairs of tiles exist where the second tile is greater than the first.
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Draw a set of two tiles that sum to 10, when drawing without replacement.
- Here, we need to identify pairs of tiles that add up to 10 and calculate the probability of drawing them without replacement.
Now, let's go ahead and match these events to the corresponding probabilities. Would you like me to calculate the exact probabilities for these events?
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Math Problem Analysis
Mathematical Concepts
Combinatorics
Probability
Conditional Probability
Counting Methods
Formulas
Combinatorial formulas for drawing without replacement
Conditional Probability formula
Theorems
Basic Probability Theorem
Counting Principle
Suitable Grade Level
Grades 9-12
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