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Solution |
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1) Kamal is throwing a dart at a circular dart board with radius 1 foot. His eyes are closed and it is just as likely the dart will strike one part of the board as another. What is the probability that the dart will stick closer to the edge than to the center?
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We must compute the relative areas of a circular board with half the board radius to the whole board.
- Dart board area =
- Half-radius board area = / 4
- Probability = whole board area - half-radius board area/ whole board area = 3/4
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2) George has two counters in his pocket. They are the same size only one is red on both sides and one is red on one side and blue on the other. He pulls one counter out of his pocket without looking and puts it on the table. If the side showing is red, what is the probability that the other side is blue?
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The unseen 3 sides are red, red, and blue.
The probability of a blue side is 1/3
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3)
The lowest number in a set of five numbers is 10. The range is 60 and the mean is 40. What is
the biggest the median could be?
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- The highest number is 70 (10 + the range).
- In order to maximize the median, the second number must be equal to the lowest number, like this:
(M = the median, N = the other number):
10 10 M N 70
- Now, in order to maximize M, N must be as low as possible to maintain the mean of 40, so that value of N is equal to M:
10 10 M M 70
- For the mean to be 40, the 2 Ms must add to 110. Therefore, M must be 55
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