Let be a sample space associated with an experiment. How many subsets of S contain either the number 2 or the number 1?

Question

Let  be a sample space associated with an experiment. How many subsets of S contain either the number 2 or the number 1?

Quizplus · Accepted Answer

To find the number of subsets that contain either 2 or 1, we can first find the total number of subsets and subtract the number of subsets that do not contain 1 or 2.

The total number of subsets of a set with n elements is 2^n. In this case, there are 11 elements, so the total number of subsets is 2^11 = 2048.

The number of subsets that do not contain 1 or 2 can be found by considering the remaining 9 elements. Each of these can either be in the subset or not, giving 2 options for each element and a total of 2^9 = 512 possible subsets.

Therefore, the number of subsets that contain either 1 or 2 is 2048 - 512 = 1536.

To check our work, we can also count the number of subsets that contain both 1 and 2. There are 9 remaining elements, and we need to choose subsets from these, so the number of subsets that contain both 1 and 2 is 2^9 - 2 = 510.

The number of subsets that contain either 1 or 2 is therefore 1536 + 510 = 2046.

Therefore, the answer is D) 6.

Let Be a Sample Space Associated with an Experiment