A student takes a quiz consisting of 10 multiple choice ques

A student takes a quiz consisting of 10 multiple choice questions. Each question has 5 possible answers. If a student is guessing the answers at random, and the answers to different questions are independent, find the probability of the student getting at least five correct answers

Solution

Here, the probability of a correct answer is p = 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 =    10      
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   ) =    0.967206502
          
Thus, the probability of at least   5   successes is  
          
P(at least   5   ) =    0.032793498 [ANSWER]