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 | 19 | 2 |\n| did not complete the homework | 3 | 6 |
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 a student passed the test and $B$ be the event that a student completed the homework. Then $P(A|B)=\frac{n(A\cap B)}{n(B)}$, where $n(A\cap B)$ is the number of students who passed the test and completed the homework, and $n(B)$ is the number of students who completed the homework.
Step2: Identify relevant values
We see from the table that $n(A\cap B) = 19$ (the number of students who passed the test and completed the homework) and $n(B)=19 + 2=21$ (the total number of students who completed the homework).
Step3: Calculate the probability
$P(A|B)=\frac{19}{21}$.
Answer:
$\frac{19}{21}$