A school contains students in grades 1,2,3,4,5 and 6. Grades 2,3,4,5 and 6 all contain the same number of students, but there are twice this number in grade 1.

a)If a student is selected at random from a list of all the students in the school, what is the probability that he will be in grade 3?
b)What is the probability that the selected student will be in an odd-numbered grade?

Soln:
Grades                          1     2      3     4     5    6
Number of students        2x   x      x     x     x    x     Then total number of students = 7x

a) Probability that he will be in grade 3 =  x/7x  = 1/7
b) Probability that the selected student will be in an odd-numbered grade.
The odd-numbered grades are 1, 3, and 5; Total number of students with odd-numbered grades is 2x + x + x = 4x
Probability of odd-numbered is therefore 4x/7x = 4/7