Monday, August 1, 2011

Solution for probability, Problem for sum



Thanks everyone for trying out the problem, and congrats to those who got the problem right!

Problem:
A pair of standard 6-sided dice is rolled once. The sum of the numbers rolled determines the diameter of a circle. What is the probability that the numerical value of the area of the circle is less than the numerical value of the circle's circumference.

Solution:
First of all, we need to find all the possible diameters of the circle. The question  states the numerical value of the area of the circle is less than the numerical value of the circle's circumference. If that is the case, then the radii will be less than 2 because

πr2 < 2πr
πr < 2π
r < 2 

If a pair of standard 6-sided die is rolled once, then the diameter will have to be either 2 or 3, because the lowest value you can roll is a 2, and a 4 won't work since the radii has to be less than 2.

There is only 1 possible way to roll a 2 (1,1), and 2 possible ways to roll a 3 (1,2) (2,1).

There are 3 possible rolls out of 36 (6*6) different rolls. Thus, the answer is 1/12.

Here's the next problem:
Problem:
At a competition with N players, the number of players given elite status is equal to 21+⌊log2(N-1)⌋ - N. Suppose that 19 players are given elite status. What is the sum of the two smallest possible values of N?

⌊x⌋ is the nearest integer ≤ x

Good luck! and remember, no calculators are allowed. :)

23 comments:

  1. Ah maths, how I used to like you.. I learnt maths in Welsh :')

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  2. Great post, but i just don.t get math. I come here alot to get some summer review before school. :)

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  3. moment... what?
    maybe i should go to school again ^^

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  4. Let's go zero for three. 34. the lowest possible numbers are prime. 17 and 17.

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  5. Hah! I actually got the dice one. Guess I'll see if my winning streak continues

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  6. This is helping me remember my calculus hahaha

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  7. This is of great help for reactivating my brain in the morning. Truly appreciated.

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  8. "no calculators are allowed." Boooo! Just kidding, gotta keep my brain fresh :p

    +followed :)

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  9. All this math... it makes my head hurt!

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  10. i cant figure it out. me stupid

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  11. I love math but it is currently the summer so my brain has clocked out ill hit you problems up in about two weeks for some fun:)

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  12. my head hurts when i try to understand :(

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  13. Math makes me feel like the class moron. I'm much more of a writing sort of person.

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  14. I can't see log that I start screaming. Hate this shit. hahaha

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  15. I have only done log with a calculator.

    Whats the answer?

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  16. waiting for an answer save me from this.

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  17. Since school opening is just around the corner this is might be really a good help. Bookmarked this one. :D buy aion accounts

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