in a class of students, the following data table summarizes how many students passed a test and completed…

in a class of students, the following data table summarizes how many students passed a test and completed the homework due the day of the test. what is the probability that a student passed the test given that they completed the homework?\n| | passed the test | failed the test |\n|--|--|--| \n| completed the homework | 14 | 3 |\n| did not complete the homework | 4 | 6 |

in a class of students, the following data table summarizes how many students passed a test and completed the homework due the day of the test. what is the probability that a student passed the test given that they completed the homework?\n| | passed the test | failed the test |\n|--|--|--| \n| completed the homework | 14 | 3 |\n| did not complete the homework | 4 | 6 |

Answer

Explanation:

Step1: Identify relevant numbers

The number of students who completed the homework and passed the test is 14, and the number of students who completed the homework (passed + failed) is (14 + 3=17).

Step2: Use conditional - probability formula

The formula for conditional probability (P(A|B)=\frac{P(A\cap B)}{P(B)}). In the context of frequency data, if (A) is the event of passing the test and (B) is the event of completing the homework, then (P(A|B)=\frac{n(A\cap B)}{n(B)}), where (n(A\cap B)) is the number of elements in (A\cap B) and (n(B)) is the number of elements in (B). So the probability is (\frac{14}{14 + 3}).

Answer:

(\frac{14}{17})