Question

In a class of students, the following data table summarizes how many students passed a test and complete the homework due the day of the test. What is the probability that a student chosen randomly from the class passed the test or completed the homework?
Passed the test Failed the test Total
Completed the homework 15 2 17
Did not complete the homework 3 7 10
Total 18 9 27

Answer 1

20 / 27 is the probability that a student chosen randomly from the class passed the test or completed the homework.

Step-by-step explanation:

To find the probability that a student chosen randomly from the class passed the test or complete the homework :

Let us take,

• Event A ⇒ a student chosen randomly from the class passed the test
• Event B ⇒ a student chosen randomly from the class complete the homework

We need to find out P (A or B) which is given by the formula,

⇒ P (A or B) = P(A) + P(B) - P(A∪B)

From the given table of data,

• The total number of students in the class = 27 students.
• The no.of students passed the test ⇒ 15+3 = 18 students.

P(A) = No.of students passed / Total students in the class

P(A) ⇒ 18 / 27

• The no.of students completed the homework ⇒ 15+2 = 17 students.

P(B) = No.of students completed the homework / Total students in the class

P(B) ⇒ 17 / 27

• The no.of students who passes the test and completed the homework = 15 students.

P(A∪B) = No.of students both passes and completes the homework / Total

P(A∪B) ⇒ 15 / 27

Therefore, to find out the P (A or B) :

⇒ P(A) + P(B) - P(A∪B)

⇒ (18 / 27) + (17 / 27) - (15 / 27)

⇒ 20 / 27

∴ The P (A or B) is 20/27.