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 who passed the test completed the homework?\n| | passed the test | failed the test |\n|--|--|--|\n| completed the homework | 16 | 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 who passed the test completed the homework?\n| | passed the test | failed the test |\n|--|--|--|\n| completed the homework | 16 | 3 |\n| did not complete the homework | 4 | 6 |

Answer

Explanation:

Step1: Find number of students who passed

The number of students who passed is the sum of those who passed and completed homework and those who passed and did not complete homework. So, $16 + 4=20$.

Step2: Find number of students who passed and completed homework

The number of students who passed and completed homework is 16.

Step3: Calculate the conditional - probability

The probability that a student who passed the test completed the homework is given by the formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of counts, it is the number of students who passed and completed homework divided by the number of students who passed. So the probability is $\frac{16}{20}=\frac{4}{5}=0.8$.

Answer:

$0.8$