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 15 3Does 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 15 3Does not have an A 2 8
Solution 1
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).
Here, event A is the event that a student has an A, and event B is the event that the student is female.
From the data table, we can see that:
- The total number of students is 15 (females with A) + 3 (males with A) + 2 (females without A) + 8 (males without A) = 28 students.
- The number of females is 15 (with A) + 2 (without A) = 17.
- The number of females with an A is 15.
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) = 15 / 17 = 0.882, or 88.2%.
So, the probability that a student has an A given that the student is female is 88.2%.
Solution 2
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).
Here, event A is "student has an A" and event B is "student is female".
From the table, we can see that:
- The total number of students is 15 (females with A) + 3 (males with A) + 2 (females without A) + 8 (males without A) = 28 students.
- The number of females is 15 (with A) + 2 (without A) = 17.
- The number of females with an A is 15.
So, we can substitute these values into the formula:
P(A|B) = P(A ∩ B) / P(B) = (number of
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