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|00000000| 03 41 53 6c 6f 74 20 4d | 61 63 68 69 6e 65 20 43 |.ASlot M|achine C|
|00000010| 6c 69 6e 69 63 0d 56 69 | 73 69 74 20 77 77 77 2e |linic.Vi|sit www.|
|00000020| 70 6f 6c 79 6d 61 74 68 | 6c 6f 76 65 2e 63 6f 6d |polymath|love.com|
|00000030| 20 66 6f 72 20 6f 74 68 | 65 72 20 66 72 65 65 20 | for oth|er free |
|00000040| 61 6e 64 20 6c 6f 77 2d | 63 6f 73 74 20 4d 61 74 |and low-|cost Mat|
|00000050| 68 65 6d 61 74 69 63 73 | 20 70 72 6f 67 72 61 6d |hematics| program|
|00000060| 73 20 66 6f 72 20 6d 69 | 64 64 6c 65 20 73 63 68 |s for mi|ddle sch|
|00000070| 6f 6f 6c 20 73 74 75 64 | 65 6e 74 73 2e 0d 0d 41 |ool stud|ents...A|
|00000080| 6e 73 77 65 72 73 0d 41 | 6c 6c 20 70 72 6f 62 61 |nswers.A|ll proba|
|00000090| 62 69 6c 69 74 69 65 73 | 20 6d 75 73 74 20 62 65 |bilities| must be|
|000000a0| 20 65 6e 74 65 72 65 64 | 20 61 73 20 72 65 64 75 | entered| as redu|
|000000b0| 63 65 64 20 66 72 61 63 | 74 69 6f 6e 73 2e 0d 0d |ced frac|tions...|
|000000c0| 54 68 72 65 65 20 41 70 | 70 6c 65 73 0d 46 69 6e |Three Ap|ples.Fin|
|000000d0| 64 20 74 68 65 20 70 72 | 6f 62 61 62 69 6c 69 74 |d the pr|obabilit|
|000000e0| 79 20 6f 66 20 67 65 74 | 74 69 6e 67 20 61 6e 20 |y of get|ting an |
|000000f0| 61 70 70 6c 65 20 6f 6e | 20 65 61 63 68 20 77 68 |apple on| each wh|
|00000100| 65 65 6c 2e 20 49 6e 20 | 74 68 65 20 65 78 61 6d |eel. In |the exam|
|00000110| 70 6c 65 20 61 74 20 74 | 68 65 20 72 69 67 68 74 |ple at t|he right|
|00000120| 20 74 68 65 20 70 72 6f | 62 61 62 69 6c 69 74 69 | the pro|babiliti|
|00000130| 65 73 20 61 72 65 20 35 | 2f 38 2c 20 31 2f 32 2c |es are 5|/8, 1/2,|
|00000140| 20 61 6e 64 20 36 2f 37 | 2e 0d 4d 75 6c 74 69 70 | and 6/7|..Multip|
|00000150| 6c 79 20 74 68 65 20 74 | 68 72 65 65 20 70 72 6f |ly the t|hree pro|
|00000160| 62 61 62 69 6c 69 74 69 | 65 73 20 74 6f 67 65 74 |babiliti|es toget|
|00000170| 68 65 72 2e 20 45 78 70 | 72 65 73 73 20 74 68 65 |her. Exp|ress the|
|00000180| 20 61 6e 73 77 65 72 20 | 61 73 20 61 20 72 65 64 | answer |as a red|
|00000190| 75 63 65 64 20 66 72 61 | 63 74 69 6f 6e 2e 20 28 |uced fra|ction. (|
|000001a0| 35 2f 38 29 28 31 2f 32 | 29 28 36 2f 37 29 20 3d |5/8)(1/2|)(6/7) =|
|000001b0| 20 33 30 2f 31 31 32 20 | 3d 20 31 35 2f 35 36 2e | 30/112 |= 15/56.|
|000001c0| 0d 0d 4e 6f 20 41 70 70 | 6c 65 73 0d 46 69 6e 64 |..No App|les.Find|
|000001d0| 20 74 68 65 20 70 72 6f | 62 61 62 69 6c 69 74 79 | the pro|bability|
|000001e0| 20 6f 66 20 6e 6f 74 20 | 67 65 74 74 69 6e 67 20 | of not |getting |
|000001f0| 61 6e 20 61 70 70 6c 65 | 20 6f 6e 20 65 61 63 68 |an apple| on each|
|00000200| 20 77 68 65 65 6c 2e 20 | 49 6e 20 74 68 65 20 65 | wheel. |In the e|
|00000210| 78 61 6d 70 6c 65 20 61 | 74 20 74 68 65 20 72 69 |xample a|t the ri|
|00000220| 67 68 74 20 74 68 65 20 | 70 72 6f 62 61 62 69 6c |ght the |probabil|
|00000230| 69 74 69 65 73 20 61 72 | 65 20 33 2f 38 2c 20 31 |ities ar|e 3/8, 1|
|00000240| 2f 32 2c 20 61 6e 64 20 | 31 2f 37 2e 0d 4d 75 6c |/2, and |1/7..Mul|
|00000250| 74 69 70 6c 79 20 74 68 | 65 20 74 68 72 65 65 20 |tiply th|e three |
|00000260| 70 72 6f 62 61 62 69 6c | 69 74 69 65 73 20 74 6f |probabil|ities to|
|00000270| 67 65 74 68 65 72 2e 20 | 45 78 70 72 65 73 73 20 |gether. |Express |
|00000280| 74 68 65 20 61 6e 73 77 | 65 72 20 61 73 20 61 20 |the answ|er as a |
|00000290| 72 65 64 75 63 65 64 20 | 66 72 61 63 74 69 6f 6e |reduced |fraction|
|000002a0| 2e 20 0d 28 33 2f 38 29 | 28 31 2f 32 29 28 31 2f |. .(3/8)|(1/2)(1/|
|000002b0| 37 29 20 3d 20 33 2f 31 | 31 32 2e 0d 0d 41 74 20 |7) = 3/1|12...At |
|000002c0| 4c 65 61 73 74 20 4f 6e | 65 20 41 70 70 6c 65 0d |Least On|e Apple.|
|000002d0| 54 61 6b 65 20 74 68 65 | 20 70 72 6f 62 61 62 69 |Take the| probabi|
|000002e0| 6c 69 74 79 20 6f 66 20 | 6e 6f 74 20 67 65 74 74 |lity of |not gett|
|000002f0| 69 6e 67 20 61 6e 20 61 | 70 70 6c 65 20 28 73 65 |ing an a|pple (se|
|00000300| 65 20 74 68 65 20 61 62 | 6f 76 65 20 73 65 63 74 |e the ab|ove sect|
|00000310| 69 6f 6e 29 20 61 6e 64 | 20 73 75 62 74 72 61 63 |ion) and| subtrac|
|00000320| 74 20 69 74 20 66 72 6f | 6d 20 6f 6e 65 2e 0d 31 |t it fro|m one..1|
|00000330| 20 2d 20 33 2f 31 31 32 | 20 3d 20 31 30 39 2f 31 | - 3/112| = 109/1|
|00000340| 31 32 2e 00 0c 00 00 00 | 00 00 10 00 0c 00 01 01 |12......|........|
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|00000380| 99 00 00 00 84 00 10 00 | 0c 00 01 00 00 00 0c 00 |........|........|
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|000003b0| 0c 00 01 00 00 00 0c 00 | 00 00 00 00 00 00 00 01 |........|........|
|000003c0| c0 00 10 00 0c 00 01 01 | 00 00 0c 33 33 00 00 99 |........|...33...|
|000003d0| 99 00 00 01 c9 00 10 00 | 0c 00 01 00 00 00 0c 00 |........|........|
|000003e0| 00 00 00 00 00 00 00 01 | e2 00 10 00 0c 00 01 01 |........|........|
|000003f0| 00 00 0c 00 00 00 00 00 | 00 00 00 01 e5 00 10 00 |........|........|
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|00000410| bb 00 10 00 0c 00 01 01 | 00 00 0c 33 33 00 00 99 |........|...33...|
|00000420| 99 00 00 02 cd 00 10 00 | 0c 00 01 00 00 00 0c 00 |........|........|
|00000430| 00 00 00 00 00          |                         |.....   |        |
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