To find the probability that a randomly selected student is taking either a Statistics class or a French class, we can use the principle of inclusion-exclusion in probability.
Let's define the following probabilities:
- \( P(A) \): The probability that a student is taking a Statistics class.
- \( P(B) \): The probability that a student is taking a French class.
- \( P(A \cap B) \): The probability that a student is taking both Statistics and French classes.
From the given information:
- \( P(A) = 0.72 \)
- \( P(B) = 0.75 \)
- \( P(A \cap B) = 0.64 \)
The formula for the union of two probabilities, which represents the probability of either event A or event B occurring, is:
[tex]\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \][/tex]
Now, substituting the given probabilities into this formula:
[tex]\[ P(A \cup B) = 0.72 + 0.75 - 0.64 \][/tex]
Performing the calculation:
[tex]\[ P(A \cup B) = 0.72 + 0.75 - 0.64 = 0.83 \][/tex]
Therefore, the probability that a randomly selected student is taking either a Statistics class or a French class is [tex]\( 0.83 \)[/tex] or 83%.
