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In a class of students, the following data table summarizes the gender of the students and whether they have an A in the class. What is the probability that a student has an A given that the student is female?Female MaleHas an A 16 4Does not have an A 2 8

Question

In a class of students, the following data table summarizes the gender of the students and whether they have an A in the class. What is the probability that a student has an A given that the student is female?Female MaleHas an A 16 4Does not have an A 2 8

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Solution

To calculate the probability that a student has an A given that the student is female, we need to use the formula for conditional probability. The formula is P(A|B) = P(A ∩ B) / P(B).

In this case, event A is a student having an A, and event B is the student being female.

From the data table, we can see that:

  • The total number of students is 16 (females with A) + 4 (males with A) + 2 (females without A) + 8 (males without A) = 30 students.
  • The number of females is 16 (with A) + 2 (without A) = 18 females.
  • The number of females with an A is 16.

So, we can substitute these values into the formula:

P(A|B) = P(A ∩ B) / P(B) = (number of females with an A) / (total number of females) = 16 / 18 = 0.8889.

So, the probability that a student has an A given that the student is female is approximately 0.89, or 89%.

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