Question

A computer is programmed to generate a sequence of three digits, where each digit is either 0 or 1, and each of these is equally likely to occur. Construct a sample space that shows all possible three-digit sequences of 0s and 1s and then find the probability that a sequence will contain exactly one 0.

Answer 1

The probability that a sequence will contain exactly one 0 is 3/8.

Explanation:

We should consider sequences of three digits, where each digit is either 0 or 1. A sequence has three places _ _ _, where each place has two possibilities, i.e., 0 or 1, so, for the multiplication rule we know that the sample space will have (2)(2)(2) = 8 sample points. Specifically the sample space is S = {111, 110, 101, 011, 100, 010, 001, 000}, there are three sequences with exactly one 0. Therefore the probability that a sequence will contain exactly one 0 is 3/8.

Answer 2

Base the question is asking to compute or calculate the probability that the sequence will contain exactly one 0, and in my further computation, the possible probability that the sequence will contain one zero would be 3/8. I hope you are satisfied with my answer and feel free to ask for more