spcs:summer2014:day_10

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spcs:summer2014:day_10 [2014/07/07 15:47] ffpaladin [Assignment] |
spcs:summer2014:day_10 [2015/07/05 16:35] (current) ffpaladin [Assignment] |
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Math Probability Problem (Optional Challenge) | Math Probability Problem (Optional Challenge) | ||

- | There is an urn containing three balls. Each ball is either red or blue, and two balls have the same color. So, there | + | There is an urn containing three balls. Each ball is either red or blue, and two balls have the same color. So, there are two possibities: either two balls are red and one is blue (the “majority-red case”) or two balls are blue and one is red (the “majority-blue” case). The probability of both cases is the same, i.e., 50%. |

- | are two possibities: either two balls are red and one is blue (the “majority-red case”) or two balls are blue and one | + | John is allowed to draw a random ball from the urn, look at it, and put it back. Then, he has to make a guess as to whether he thinks the urn is majority-blue or majority-red. Let’s say that John has drawn a red ball. It seems |

- | is red (the “majority-blue” case). The probability of both cases is the same, i.e., 50%. | + | |

- | John is allowed to draw a random ball from the urn, look at it, and put it back. Then, he has to make a guess as to | + | |

- | whether he thinks the urn is majority-blue or majority-red. Let’s say that John has drawn a red ball. It seems | + | |

natural that John should guess that the urn is probably majority-red. We now ask you to confirm this is a good | natural that John should guess that the urn is probably majority-red. We now ask you to confirm this is a good | ||

guess, using Bayes’ rule. | guess, using Bayes’ rule. | ||

- | Let “MajRed” be the event that the urn is majority-red. So, “not MajRed” is the event that the urn is not majorityred, which means that the urn is majority-blue. Let “RedBall” be the event that John picked a red ball. We are | + | Let “MajRed” be the event that the urn is majority-red. So, “not MajRed” is the event that the urn is not majorityred, which means that the urn is majority-blue. Let “RedBall” be the event that John picked a red ball. We are interested in the probability P(MajRed|RedBall) that the urn is majority-red given that John has picked a red ball. |

- | interested in the probability P(MajRed|RedBall) that the urn is majority-red given that John has picked a red ball. | + | |

* (a) What is the prior probability P(MajRed) according to the above description? | * (a) What is the prior probability P(MajRed) according to the above description? |

/soe/sherol/.html/teaching/data/pages/spcs/summer2014/day_10.txt · Last modified: 2015/07/05 16:35 by ffpaladin