a test was given to a group of students. the grades and gender are summarized below.\n| | a | b | c | total…

a test was given to a group of students. the grades and gender are summarized below.\n| | a | b | c | total |\n|--|--|--|--|--|\n| male | 4 | 17 | 5 | 26 |\n| female | 15 | 13 | 14 | 42 |\n| total | 19 | 30 | 19 | 68 |\nif one student is chosen at random from those who took the test, find the probability that the student was male given they got a c. round answer to three decimal places.

a test was given to a group of students. the grades and gender are summarized below.\n| | a | b | c | total |\n|--|--|--|--|--|\n| male | 4 | 17 | 5 | 26 |\n| female | 15 | 13 | 14 | 42 |\n| total | 19 | 30 | 19 | 68 |\nif one student is chosen at random from those who took the test, find the probability that the student was male given they got a c. round answer to three decimal places.

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, let $A$ be the event that the student is male and $B$ be the event that the student got a 'C'. Then $P(A|B)=\frac{n(A\cap B)}{n(B)}$, where $n(A\cap B)$ is the number of male students who got a 'C' and $n(B)$ is the total number of students who got a 'C'.

Step2: Identify values from the table

From the table, $n(A\cap B)$ (number of male students who got a 'C') is 5, and $n(B)$ (total number of students who got a 'C') is 19.

Step3: Calculate the probability

$P(A|B)=\frac{5}{19}\approx 0.263$

Answer:

$0.263$