A multiple choice exam has ten questions Each question has f

A multiple choice exam has ten questions. Each question has five possible answers, of which one is correct. Suppose that a student did not study for the exam, that is, the student guesses on every question so that the probability of success is 0.20. What is the probability that the student answers at least seven questions correctly?

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 =    10      
p = the probability of a success =    0.2      
x = our critical value of successes =    7      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   6   ) =    0.999135642
          
Thus, the probability of at least   7   successes is  
          
P(at least   7   ) =    0.000864358 [ANSWER]