A student has not been to class and must pass a 20 question

A student has not been to class and must pass a 20 question true/false exam to continue in the course. The student will guess on every question and must get at least 14 correct to pass the test. What is the probability that the student will pass the test?

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 =    20      
p = the probability of a success =    0.5      
x = our critical value of successes =    14      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   13   ) =    0.942340851
          
Thus, the probability of at least   14   successes is  
          
P(at least   14   ) =    0.057659149 [ANSWER]