A student guesses on every question of a multiplechoice test

A student guesses on every question of a multiple-choice test that has 7 question, each with 5 possible answers. What is the probability that the student will get at least 5 of the questions right?

Solution

The probability of a correct answer is 1/5 = 0.2.

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 =    7      
p = the probability of a success =    0.2      
x = our critical value of successes =    5      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   4   ) =    0.995328
          
Thus, the probability of at least   5   successes is  
          
P(at least   5   ) =    0.004672 [ANSWER]