To find the probability that an applicant has a master's degree given that they have teaching experience, we will use the concept of conditional probability. The conditional probability of an event B given that event A has occurred is denoted as P(B|A) and can be calculated using the formula:
\[ P(B|A) = \frac{P(A \cap B)}{P(A)} \]
Here, we want to find P(Master's Degree | Teaching Experience).
From the information given, we have:
- P(Teaching Experience) = 70% or 0.70,
- P(Master's Degree) = 54% or 0.54,
- P(Both Teaching Experience and Master's Degree) = 32% or 0.32.
Now, P(Master's Degree | Teaching Experience) will be calculated as follows:
\[ P(Master's Degree | Teaching Experience) = \frac{P(Teaching Experience \cap Master's Degree)}{P(Teaching Experience)} \]
Substituting the given values, we get:
\[ P(Master's Degree | Teaching Experience) = \frac{0.32}{0.70} \]
Now, divide 0.32 by 0.70:
\[ P(Master's Degree | Teaching Experience) \approx 0.4571 \]
Therefore, the probability that an applicant has a master's degree, given that they have teaching experience, is approximately 45.71%.
