Four students attempt to register online at the same time for an Introductory Statistics class that is full. Two are on the football team and two are on the basketball team. They are put on a wait list. Prior to the start of the semester, two enrolled students drop the course, so the professor randomly selects two of the four wait list students and gives them seats in the class. What is the probability that both students selected play the same sport?
Accepted Solution
A:
Answer: [tex]\dfrac{1}{6}[/tex]Step-by-step explanation:Given : The number of students attempt to register : n = 4Two are on the football team and two are on the basketball team. The number of ways to select 2 students out of 4 (order doesn't matter) is given by :-[tex]^4C_2=\dfrac{4!}{2!(4-2)!}=\dfrac{4\times3\times2\times1}{2\times2}=6[/tex] (1)The number of ways to select 2 students who play same sport :-[tex]^2C_2=\dfrac{2!}{2!(2-2)!}=1[/tex] (2)Now divide (1) by (2) we get,The probability that both students selected play the same sport :-[tex]=\dfrac{1}{6}[/tex]