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 is a male given that they have an a?\n| |female|male|\n|--|--|--|\n|has an a|8|11|\n|does not have an a|7|2|\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 is a male given that they have an a?\n| |female|male|\n|--|--|--|\n|has an a|8|11|\n|does not have an a|7|2|\nanswer attempt 1 out of 2

Answer

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In the context of this problem, we want to find $P(\text{Male}|\text{Has an A})$, so $P(\text{Male}|\text{Has an A})=\frac{\text{Number of male students with an A}}{\text{Total number of students with an A}}$.

Step2: Calculate the total number of students with an A

The number of female students with an A is 8 and the number of male students with an A is 11. So the total number of students with an A is $8 + 11=19$.

Step3: Calculate the probability

The number of male students with an A is 11. Using the conditional - probability formula, $P(\text{Male}|\text{Has an A})=\frac{11}{19}$.

Answer:

$\frac{11}{19}$