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?\n| |female|male|\n|--|--|--|\n|has an a|4|2|\n|does not have an a|5|19|\nanswer attempt 1 out of 2

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?\n| |female|male|\n|--|--|--|\n|has an a|4|2|\n|does not have an a|5|19|\nanswer attempt 1 out of 2

Answer

Explanation:

Step1: Find total number of females

Add the number of females with an A and without an A. $4 + 5=9$.

Step2: Find number of females with an A

It is 4 from the table.

Step3: Calculate conditional - probability

The formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of counts, if event A is having an A and event B is being female, the probability that a student has an A given that the student is female is $\frac{\text{Number of females with an A}}{\text{Total number of females}}$. So $P=\frac{4}{9}$.

Answer:

$\frac{4}{9}$