# 11: 10. Bernoulli Processes

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$

The following topics are included in the seven videos below.

1. Intro to Bernoulli Processes
2. Bernoulli Processes, Example 1 and definitions
3. Bernoulli Processes, Example 2
4. Bernoulli Processes, Example 3
5. Bernoulli Processes, Example 4 (with conditional)
6. Bernoulli Processes, Example 5 (using a complement)
7. Bernoulli Processes, Example 6 (with conditional)

#### Prework

1. A fair die is tossed five times. Find the probability of throwing four sixes.

2. A fair die is tossed five times. Find the probability of throwing at least 1 six.

3. The patrons at a certain library check out only fiction books 70% of the time. Assume that the visits to the library are independent. What is the probability that 20 of the next 25 patrons will check out only fiction books?

11: 10. Bernoulli Processes is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.