# How do you find how many bit strings of length 6 are there?

(a) How many bit strings of length 6 are there? Explain.

(b) How many bit strings of length 6 are there which begin with a 0 and end with a 1? Explain.

(c) How many bit strings of length 6 start with a 1 bit or end with a 0 bit? Explain.

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#### Solution Preview

(a) There are 2^6=64 different bit strings of length 6. The easiest way to see this is to notice that each of the 6 different bit positions in the string has 2 possible values, 0 or 1. Since each of these choices is independent of the other we have ...

#### Solution Summary

This solution explains how to do the required calculations in 198 words with work and the answers.

Expected Value: Discrete Structures

See the attached file.

1. How many bit strings of length ten contain either at least five consecutive 0's or at least five consecutive 1's? explain

2. Which is more likely: rolling a total of 8 when two dice are rolled, or rolling a total of 8 when three dice are rolled? explain

3. Three fair dice are rolled.Let X be the sum of the numbers that come up. Find the expected value EX and the variance VarX.

See attachment for problem 4.

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