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10. Bernoulli Processes

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    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)










    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?

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    1. A success is throwing a six while a failure is throwing anything else. On one toss, the probability of throwing a six is \(\frac{1}{6}\) so \(p=\frac{1}{6}\) and therefore \(1-p=\frac{5}{6}\). We roll the die \(5\) times so \(n=5\) and we want four sixes, so \(r=4\). Therefore, Pr(four sixes)\(=C(5,4)\cdot (\frac{1}{6})^4\cdot (\frac{5}{6})^1\).
    2. Everything is the same as in problem 1, except that \(r=1,2,3,4,5\). We could plug each of these into the formula and add them together, or we we can use the complement. In the complement, \(r=0\). Therefore Pr(at least 1 six)\(=1-C(5,0)\cdot (\frac{1}{6})^0\cdot (\frac{5}{6})^5\).
    3. A success is a library patron checking out only fiction while a failure is a library patron not checking out only fiction. We also see that \(p=0.7, 1-p=0.3, n=25\) and \(r=20\). So Pr(20 check out only fiction)\(=C(25,20)\cdot (0.7)^{20}\cdot (0.3)^5\).

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

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