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|

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|

Answer

Explanation:

Step1: Calculate total female students

The total number of female students is the sum of female students with an A and those without an A. So, $4 + 5=9$.

Step2: Apply conditional - probability formula

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

Answer:

$\frac{4}{9}$