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Geometric Probability and Expected Value

Geometric Probability and Expected Value. Jim Rahn www.jamesrahn.com James.Rahn@verizon.net. A Warm Up Activity.

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Geometric Probability and Expected Value

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  1. Geometric Probability and Expected Value Jim Rahn www.jamesrahn.com James.Rahn@verizon.net

  2. A Warm Up Activity A dart board consists of five concentric circles. The width of each of the rings is the same. If a dart is randomly launched at the dart board and it lands on the board. What is the probability the dart lands in each region?

  3. Theoretical Solution Using Geometry A dart board consists of five concentric circles. The width of each of the rings is the same. If a dart is randomly thrown at the dart board and it lands on the board. What is the probability the dart lands in each region?

  4. Simulating the Tossing of the Darts Can we simulate tossing a dart at this dart board through a probability experiment? Place labeled disks (or cubes) with the indicated number of disks into a bag. Draw one disk at a time, record result, return disk to the bag. Repeat 100 times Experimental Results

  5. Simulating the Tossing of the Darts Possible results Experimental Results

  6. Simulating the Tossing of the Darts- Method 2 Simulating the Toss with the graphing calculator Use random number generator on calculator randInt(1,25,5) A = 1 B = 2, 3, 4 C = 5, 6, 7, 8, 9 D = 10, 11, 12, 13, 14, 15, 16 E = 17, 18, 19, 20, 21, 22, 23, 24, 25 Select and classify 100 numbers Experimental Results

  7. Simulating the Tossing of the Darts- Method 2 Possible results Experimental Results

  8. Expected Value A dart board consists of five concentric circles. The width of each of the rings is the same. If a dart is randomly launched at the dart board and it lands on the board. What is the probability the dart lands in each region? FAIR GAME? Pay $1 to toss a dart. Hit A: Get back $3 Hit B: Get back $2 Hit C: Get back $1 Hit D or E: Lose $1

  9. Expected Value You are at a state fair and are offered a “Game of Chance.” You pay $1 to toss a dart at this dartboard. Hit A: Get back $3, Hit B: Get back $2, Hit C: Get back $1 Hit D or E: Lose $1 Is this a “FAIR GAME?“

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