Math Problem Statement
Solution
To find , we need to calculate the probability that a board is of size given that it is made of Oak.
Using conditional probability:
From the table:
- The number of 1"x2" Oak boards is .
- The total number of Oak boards is .
Therefore,
So, the answer is or approximately as a decimal.
Would you like further details on conditional probabilities, or do you have any other questions?
Here are some related questions for further exploration:
- What is the probability of selecting a Maple board given it's 1"x4"?
- Calculate .
- What is the probability of choosing a board that is 1"x2" regardless of wood type?
- How would the probability change if more Oak boards were added?
- How can we determine if board size and wood type are independent?
Tip: In probability, conditional probability helps narrow down the sample space by focusing on a specific subset of interest.
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Math Problem Analysis
Mathematical Concepts
Probability
Conditional Probability
Two-Way Frequency Tables
Formulas
P(A | B) = (Number of favorable outcomes) / (Total outcomes for condition)
Theorems
Conditional Probability Theorem
Suitable Grade Level
Grades 7-10
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