Math Problem Statement

Find P("1"x2" | Oak). Give your answer as a fraction or a decimal.

Solution

To find P("1x¨2 ¨| Oak")P(\text{"1\"x2\" | Oak"}), we need to calculate the probability that a board is of size 1"x2"\text{1"x2"} given that it is made of Oak.

Using conditional probability: P("1x¨2 ¨| Oak")=Number of 1"x2" Oak boardsTotal number of Oak boardsP(\text{"1\"x2\" | Oak"}) = \frac{\text{Number of 1"x2" Oak boards}}{\text{Total number of Oak boards}}

From the table:

  • The number of 1"x2" Oak boards is 22.
  • The total number of Oak boards is 1111.

Therefore, P("1x¨2 ¨| Oak")=211P(\text{"1\"x2\" | Oak"}) = \frac{2}{11}

So, the answer is 211\frac{2}{11} or approximately 0.18180.1818 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:

  1. What is the probability of selecting a Maple board given it's 1"x4"?
  2. Calculate P("1x¨3 ¨| Cherry")P(\text{"1\"x3\" | Cherry"}).
  3. What is the probability of choosing a board that is 1"x2" regardless of wood type?
  4. How would the probability change if more Oak boards were added?
  5. 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