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|3|5|\n|does not have an a|8|13|

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|3|5|\n|does not have an a|8|13|

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, if $A$ is the event that a student is male and $B$ is the event that a student has an A, then $P(A|B)=\frac{n(A\cap B)}{n(B)}$, where $n(A\cap B)$ is the number of male students with an A and $n(B)$ is the total number of students with an A.

Step2: Identify relevant values from the table

The number of male students with an A, $n(A\cap B) = 5$. The total number of students with an A is $3 + 5=8$ (sum of female and male students with an A).

Step3: Calculate the probability

$P(\text{Male}|\text{Has an A})=\frac{5}{8}$

Answer:

$\frac{5}{8}$