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a) I have three cards. One is green on both sides, one is blue on both sides, and one is green on one side and blue on the other. The cards are otherwise indistinguishable. I put the cards behind my back and shuffle them, then I pick one randomly and show you a green side. What is the probability that the other side is also green? Explain your reasoning. Hint: this can be done several ways. Basic probability is sufficient but you can also employ conditional probability.

a) I have three cards. One is green on both sides, one is blue on both sides, and one is green on one side and blue on the other. The cards are otherwise indistinguishable. I put the cards behind my back and shuffle them, then I pick one randomly and show you a green side. What is the probability that the other side is also green? Explain your reasoning. Hint: this can be done several ways. Basic probability is sufficient but you can also employ conditional probability.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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a) I have three cards. One is green on both sides, one is blue on both sides, and one is green on one side and blue on the other. The cards are otherwise indistinguishable. I put the cards behind my back and shuffle them, then I pick one randomly and show you a green side. What is the probability that the other side is also green? Explain your reasoning. Hint: this can be done several ways. Basic probability is sufficient but you can also employ conditional probability. bi) The UN security council has 15 members, 5 of which have the right to veto a proposition (a proposition is vetoed if any of those 5 members vote “no”). In order for a proposition, 9 members must vote “yes” with no vetoes. If all members vote “yes” or “no,” in how many different vote outcomes can a proposition pass? bii) What if each member can vote “yes,” “no,” or abstains (does not vote either way)? (This one is tricky, do your best)
Transcribed Image Text:a) I have three cards. One is green on both sides, one is blue on both sides, and one is green on one side and blue on the other. The cards are otherwise indistinguishable. I put the cards behind my back and shuffle them, then I pick one randomly and show you a green side. What is the probability that the other side is also green? Explain your reasoning. Hint: this can be done several ways. Basic probability is sufficient but you can also employ conditional probability. bi) The UN security council has 15 members, 5 of which have the right to veto a proposition (a proposition is vetoed if any of those 5 members vote “no”). In order for a proposition, 9 members must vote “yes” with no vetoes. If all members vote “yes” or “no,” in how many different vote outcomes can a proposition pass? bii) What if each member can vote “yes,” “no,” or abstains (does not vote either way)? (This one is tricky, do your best)
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