What is the probability of getting exactly 4 correct answers?

Question

a multiple-choice test in which each question has 4 choices only one of which is correct. Assume that 7 questions are answered by guessing randomly.
What is the probability of getting exactly 4 correct answers?

Answer 1

p = probability that a given question is answered correctly 

   = 1/4 = 0.25

q = probability that a given question is answered incorrectly 

   = 3/4 = 0.75

 

probability that exactly 4 out of 7 questions are correct 

 

    = ₇C₄(0.25)⁴(0.75)³  = 0.0577