On a 75 question multiple choice test assume 4 possible answ

On a 75 question multiple choice test (assume 4 possible answers for each question, one of which is correct), find the probability of getting 20 or more questions correct purely by guessing

Solution

Note that P(at least x) = 1 - P(at most x - 1).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    75      
p = the probability of a success = 1/4 =   0.25      
x = our critical value of successes =    20      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   19   ) =    0.587532305
          
Thus, the probability of at least   20   successes is  
          
P(at least   20   ) =    0.412467695 [ANSWER]