Question

Ms. Francis needs 2  students to read a poem, so she assigns each student in her class of 28 students a number from 1 to 28 . She then chooses 2 student numbers at random. What is the probability that Ms. Francis chooses 2 even-numbered students?

Answer 1

$\text{Total numbers of student in the class are 28.}\\ \\ \text{Ms. Francis needs 2 students to read the poem, so she assigned each}\\ \text{student a number from 1 to 28. so there will be 14 even numberd and }\\ \text{14 students with odd number.}\\ \\ \text{now she chooses 2 students at random, so the probability that the first}\\ \text{number choosen by her is an even numbered student}=\frac{14}{28}=\frac{1}{2}$

$\text{now after choosen one even numbered student, there left only 13 even}\\ \text{numberd students and total of 27 student.}\\ \text{so probability of choosing the second student is even numbered}=\frac{13}{27}\\ \\ \text{so, the probability that Ms. Francis chooses 2 even-numbered student is}\\ \\ =\frac{1}{2}\times \frac{13}{27}\\ \\ =\frac{13}{54}$

Hence the probability that the 2 students choosen are even numbered students is: 13/54