Difference between revisions of "Segment 5. Bernoulli Trials"

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====Watch this segment====
====Watch this segment====
(Don't worry, what you see out-of-focus below is not the beginning of the segment.  Press the play button to start at the beginning and in-focus.)
The direct YouTube link is [http://youtu.be/2T3KP2LleFg http://youtu.be/2T3KP2LleFg]
The direct YouTube link is [http://youtu.be/2T3KP2LleFg http://youtu.be/2T3KP2LleFg]

Latest revision as of 23:43, 26 January 2019

Watch this segment

The direct YouTube link is http://youtu.be/2T3KP2LleFg

Links to the slides: PDF file or PowerPoint file


To Compute

1. You throw a pair of fair dice 10 times and, each time, you record the total number of spots. When you are done, what is the probability that exactly 5 of the 10 recorded totals are prime?

2. If you flip a fair coin one billion times, what is the probability that the number of heads is between 500010000 and 500020000, inclusive? (Give answer to 4 significant figures.)

To Think About

1. Suppose that the assumption of independence (the first "i" in "i.i.d.") were violated. Specifically suppose that, after the first Bernoulli trial, every trial has a probability Q of simply reproducing the immediately previous outcome, and a probability (1-Q) of being an independent trial. How would you compute the probability of getting n events in N trials if the probability of each event (when it is independent) is p?

2. Try the Mathematica calculation on slide 5 without the magical "GenerateConditions -> False". Why is the output different?

Class Activity


Part 2: The problem as stated multiplies your wager by 2 on a win. What is the smallest this factor can be while still leaving the probability of ending up above one billion greater than 0.5, assuming that you play with an optimal f given the value of the factor?

Jeff's solution - updated in response to group 2's excellent work