In a math class with 19 students, a test was given the same day that an assignment was due. There were 10 students who passed the test and 11 students who completed the assignment. There were 6 students who failed the test and also did not complete the assignment. What is the probability that a student chosen randomly from the class passed the test and completed the homework?

The probability that a student is chosen randomly from the class passed the test and completed the homework will be 0.1637.

What is probability?

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

In a math class with 19 students, a test was given the same day that an assignment was due.

There were 10 students who passed the test and 11 students who completed the assignment.

There were 6 students who failed the test and also did not complete the assignment.

Then the probability that a student is chosen randomly from the class passed the test and completed the homework will be

The number of the student who has done at least one assignment or passed the test is 19 - 6 = 13

n(A) = passes student

n(B) = given assignment

Then we have

[tex]\rm n(A \cap B) = n(A) + n(B) - n(A \cup B) \\\\n(A \cap B) = 10 + 11 - 13\\\\n(A \cap B) = 8[/tex]

Then the probability will be

[tex]\rm P = \dfrac{^8C_2}{^{19}C_2}\\\\P = \dfrac{28}{171}\\\\P = 0.1637[/tex]

More about the probability link is given below.

https://brainly.com/question/795909

#SPJ2