MHB Geometric Distributions Anyone?

AI Thread Summary
The discussion focuses on a participant's struggle with question 10 related to geometric distributions, particularly in a lottery context. There is uncertainty about how to account for different time factors in the calculations. Participants emphasize that the order of events matters in this problem, which is atypical for lottery games. Guidance is sought on calculating the probability of winning on the first attempt. Clarification on these points is essential for understanding the question correctly.
nicole58
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View attachment 3720

I'm struggling with question 10. I'm not sure how to account for the different time? I'm probably just overthinking it. I have attached a picture of the answer as well.View attachment 3721

Again, trying to figure out question #10
 

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Hi nicole58,

Welcome to MHB! :)

Ok, let's start with calculating how she would win on the first try of the year. Any idea how you would do that?

It seems for this problem the order matters, which is strange for lottery type games but given the answer that is how this game is played. So what is the chance she wins the game on her very first try?
 

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Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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