Answered

IDNLearn.com: Your destination for reliable and timely answers to any question. Find reliable solutions to your questions quickly and accurately with help from our dedicated community of experts.

At Timberland High School, 72% of students are taking a Statistics class, 75% of students are taking a French class, and 64% of students are taking both.

Find the probability that a randomly selected student is taking a Statistics class or a French class. You may answer with a fraction or a decimal rounded to three places if necessary.

Sagot :

GinnyAnsweridn
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%.
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. IDNLearn.com has the solutions you’re looking for. Thanks for visiting, and see you next time for more reliable information.