We select a subset X of the set S = {1, 2,..., 100} randomly and uniformly (so that every subset has the same probability of being selected). What is the probability that (a) X has an even number of elements; (b) both 1 and 100 belong to X; (c) the largest element of S is 50; (d) S has at most 2 elements.

We select a subset X of the set S = {1, 2,..., 100} randomly and uniformly (so that every subset has the same probability of being selected). What is the probability that (a) X has an even number of elements; (b) both 1 and 100 belong to X; (c) the largest element of S is 50; (d) S has at most 2 elements.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

We select a subset X of the set S = {1, 2,..., 100} randomly and uniformly (so that every subset has the same probability of being selected). What is the probability that

(a) X has an even number of elements;

(b) both 1 and 100 belong to X;

(d) S has at most 2 elements.

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