In a survey conducted at a local high school, preferences for a new school color were measured: 58% of students liked the color blue, 45% preferred green, and 22% liked both colors. If we randomly pick a student from the school, what's the probability that they would like neither blue nor green?

To solve this problem , we need to determine the probability of a student not lik ing either blue or green . \n First , let ' s find the probability of a student lik ing neither color . Since there are only two colors to choose from , the probability of a student lik ing neither color is simply the complement of the probability of lik ing either color . \n The probability of a student lik ing either blue or green is : \n P ( blue or green ) = P ( blue ) + P ( green ) \n P ( blue or green ) = 5 8 % + 4 5 % = 1 0 3 % \n Since the probability of a student lik ing either color cannot be greater than 1 0 0 %, we know that there must be an error in the survey results . However , assuming that the survey results are correct , we can calculate the probability of a student lik ing neither color as : \n P ( ne ither ) = 1 - P ( blue or green ) \n P ( ne ither ) = 1 - 1 0 3 % \n P ( ne ither ) = 0 % \n There fore , if we randomly pick a student from the school , there is a 0 % probability that they would like neither blue nor green . </s>