in a class of students, the following data table summarizes the gender of the students and whether they have…

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?

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?

Answer

Explanation:

Step1: Recall the formula for conditional probability

The formula for conditional probability is (P(A|B)=\frac{P(A\cap B)}{P(B)}). In the context of this problem, if (A) is the event that a student has an (A) and (B) is the event that a student is female, then (P(A|B)=\frac{\text{Number of female students with an }A}{\text{Total number of female students}})

Step2: Calculate the number of female students

The number of female students is the sum of female students with an (A) and female students without an (A). So, (16 + 2=18)

Step3: Calculate the probability

We know the number of female students with an (A) is (16). Using the formula (P(A|B)=\frac{16}{18}=\frac{8}{9})

Answer:

(\frac{8}{9})