A 10-item multiple choice test with 4 options (A,B,C,D) is given to a class in English, what is the probability that the student’s answers are of the same letters

Answer 1

let's pick one of the letters, say the A
Prob(A) = 1/4
you want that to happen 10 times in a row
prob(10 A's) = (1/4)^10

but the same reasoning can be used for each of the 4 letters, so
prob(10 of the same letter) = 4(1/4)^10 = (1/4)^9