Question 641475: Over time, you have many conversations with a friend about your favorite actress, favorite musician, favorite book, favorite TV show, and so forth for 100 separate topics. On any given topic, there’s only a .02 probability that you agree. If you did agree on a topic, you would consider it to be coincidental.
a. If whether you agree on any two different topics are independent events, find the probability that you and your friend never have a coincidence on these 100 topics.
b. Find the probability that you have a coincidence on at least one topic.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Over time, you have many conversations with a friend about your favorite actress, favorite musician, favorite book, favorite TV show, and so forth for 100 separate topics. On any given topic, there’s only a .02 probability that you agree. If you did agree on a topic, you would consider it to be coincidental.
a. If whether you agree on any two different topics are independent events, find the probability that you and your friend never have a coincidence on these 100 topics.
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Ans: P(x = 0) = .98^100 = 0.1326
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b. Find the probability that you have a coincidence on at least one topic.
P(1<= x <=100) = 1 - P(x = 0) = 1-0.1326 = 0.8674
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Cheers,
Stan H.
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