Question

question
given the completed contingency table above, find the probability that a teacher has a bachelors degree given that they are an english teacher. express your answer as a fraction.
provide your answer below:

Explanation:

Step1: Recall Conditional Probability Formula

The formula for conditional probability is \( P(A|B) = \frac{P(A \cap B)}{P(B)} \). For a contingency table, this translates to \( P(\text{Bachelors} | \text{English}) = \frac{\text{Number of English teachers with Bachelors}}{\text{Total number of English teachers}} \).

Step2: Identify Values from Table

From the table, the number of English teachers with a Bachelors degree is 5, and the total number of English teachers is 15.

Step3: Calculate Probability

Substitute the values into the formula: \( \frac{5}{15} \). Simplify the fraction by dividing numerator and denominator by 5: \( \frac{5 \div 5}{15 \div 5} = \frac{1}{3} \).

Answer:

\(\frac{1}{3}\)