A set S contains 7 elements. A non-empty subset A of S and an element x of S are chosen at random. Then the probability that x A is:

Step-by-step solution

Let S = x₁, x₂, x₃, x₄, x₅, x₆, x₇ Let the chosen element be x _ i . Total number of subsets of S =2^7=128 No. of non-empty subsets of S =128-1=127 We need to find number of those subsets that contains x_i . array |l|l|l|l|l|l|l| 2 & 2 & 2 & 2 & 1 & 2 & 2 array x₁ x₂ -—- x_i=-x₇ For those subsets containing x_i , each element has 2 choices. i.e., (included or not included) in subset, However as the subset must contain x_i , x_i has only one choice. (included one) So, total no. of subsets containing x_i=2 2 2 2 1 2