chapter 4.3 homework\nscore: 28/42 answered: 23/33\nquestion 24\n0/1 pt 2 99 details\n4.3 conditional…

chapter 4.3 homework\nscore: 28/42 answered: 23/33\nquestion 24\n0/1 pt 2 99 details\n4.3 conditional probability. two - way conditional table.\ngiving a test to a group of students, the grades and gender are summarized below\n| | a | b | c | total |\n|--|--|--|--|--|\n| male | 5 | 15 | 20 | 40 |\n| female | 12 | 11 | 10 | 33 |\n| total | 17 | 26 | 30 | 73 |\nif one student is chosen at random, find the probability that the student was male given they got a c. type as a fraction.\nquestion help: message instructor

chapter 4.3 homework\nscore: 28/42 answered: 23/33\nquestion 24\n0/1 pt 2 99 details\n4.3 conditional probability. two - way conditional table.\ngiving a test to a group of students, the grades and gender are summarized below\n| | a | b | c | total |\n|--|--|--|--|--|\n| male | 5 | 15 | 20 | 40 |\n| female | 12 | 11 | 10 | 33 |\n| total | 17 | 26 | 30 | 73 |\nif one student is chosen at random, find the probability that the student was male given they got a c. type as a fraction.\nquestion help: message instructor

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 a two - way table, if $A$ is the event of being male and $B$ is the event of getting a 'C', then $P(A|B)=\frac{\text{Number of males who got a 'C'}}{\text{Total number of students who got a 'C'}}$.

Step2: Identify values from the table

From the table, the number of males who got a 'C' is 20, and the total number of students who got a 'C' is 30.

Answer:

$\frac{20}{30}=\frac{2}{3}$