The probability that a student uses Smarthinking Online Tutoring on a regular basis is 0.31 . In a group of 21 students, what is the probability that exactly 5 of them use Smarthinking Online Tutoring on a regular basis?

This is solved using the probability distribution formula for random variables where the combination formula for selection is used to determine the probability of these random variables occurring. This formula is denoted by:

P(X=r) = nCr × p^r × q^n-r

Where:

n = number of sampled variable which in this case = 21

r = variable outcome being determined which in this case = 5

p = probability of success of the variable which in this case = 0.31

q= 1- p = 1 - 0.31 = 0.69

P(X=5) = 21C5 × 0.31^5 × 0.69^16

P(X=5) = 0.0241