A student takes a 7 question multiplechoice quiz with 4 choi

A student takes a 7 question multiple-choice quiz with 4 choices for each question. If the student guesses at random on each question, what is the probability that the student gets exactly 3 questions correct? please dont skip steps. I want to know how to do problems like this not just the answer

Solution

As there are 4 choices, then the probability of getting it correctly is

p = 1/4 = 0.25

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    7      
p = the probability of a success =    0.25      
x = the number of successes =    3      
          
Thus, the probability is          
          
P (    3   ) =    0.173034668 [ANSWER]