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- Words: 278
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x 3 4 5 6
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การออกแต้มท่ีเป็ นไปได้
(1,1,1) (1,1,2) (1,1,3) (1,1,4) (1,2,3) (2,2,2) (1,1,5) (1,2,4) (1,3,3) (2,2,3) (1,1,6) (1,2,5) (1,3,4) (3,2,3) (2,2,4) (1,2,6) (1,3,5) (1,4,4) (3,2,4) (2,2,5) (3,3,3) (1,3,6) (1,5,4) (2,2,6) (3,2,5) (2,4,4) (3,4,3) (1,4,6) (1,5,5) (3,2,6) (4,2,5) (3,5,3) (3,4,4) (1,5,6) (6,2,4) (3,6,3) (4,3,5) (2,5,5) (4,4,4) (1,6,6) (6,2,5) (6,3,4) (5,4,4) (3,5,5) (6,3,5) (2,6,6) (6,4,4) (4,5,5)
(1,2,1) (1,3,1) (1,4,1) (1,3,2)
(2,1,1) (3,1,1) (1,2,2) (2,1,2) (2,2,1) (4,1,1) (2,1,3) (2,3,1) (3,1,2) (3,2,1)
(1,5,1) (1,4,2) (3,1,3) (3,2,2) (1,6,1) (1,5,2) (1,4,3) (3,3,2) (4,2,2) (1,6,2) (1,5,3) (4,4,1) (3,4,2) (5,2,2)
(5,1,1) (2,1,4) (3,3,1) (2,3,2) (6,1,1) (2,1,5) (3,1,4) (2,3,3) (2,2,4) (2,1,6) (3,1,5) (4,1,4) (2,3,4) (2,5,2)
(1,6,3) (1,4,5) (6,2,2) (3,5,2) (4,4,2) (3,3,4) (1,6,4) (5,5,1) (3,6,2) (4,5,2) (3,3,5) (4,4,3) (1,6,5) (6,4,2) (3,3,6) (4,5,3) (5,5,2)
(3,1,6) (5,1,4) (2,2,6) (2,3,5) (4,2,4) (4,3,3) (4,1,6) (5,1,5) (2,3,6) (2,4,5) (5,3,3) (4,3,4) (5,1,6) (2,6,4) (6,3,3) (3,4,5) (5,2,5)
(6,6,1) (6,5,2) (6,4,3) (4,4,5) (5,5,3) (6,5,3) (6,6,2) (4,4,6) (5,5,4)
(6,1,6) (2,6,5) (2,5,6) (5,6,2) (5,2,6) (3,6,4) (3,4,6) (4,6,3) (4,3,6) (4,5,4) (5,3,5) (3,6,5) (3,5,6) (5,6,3) (5,3,6) (6,2,6) (4,6,4) (5,4,5)
P(x) 1/216 3/216 6/216
xP(x) 3/216 12/216 30/216
10/216
60/216
(2,4,1) (4,1,2) (4,2,1)
15/216 105/216
(2,5,1) (5,1,2) (5,2,1) (3,4,1) (4,1,3) (4,3,1)
21/216 168/216
(2,6,1) (6,1,2) (6,2,1) (3,5,1) (5,1,3) (5,3,1)
25/216 225/216
(2,4,3) (4,3,2) (4,2,3)
(3,6,1) (6,1,3) (6,3,1) (5,4,1) (4,1,5) (4,5,1) 27/216 270/216 (2,5,3) (5,3,2) (5,2,3)
(4,6,1) (6,1,4) (6,4,1) (2,6,3) (6,3,2) (6,2,3) (2,5,4) (5,4,2) (5,2,4)
27/216 297/216
(5,6,1) (6,1,5) (6,5,1) (2,4,6) (4,6,2) (4,2,6) 25/216 300/216 (3,5,4) (5,4,3) (5,3,4)
21/216 273/216
15/216 210/216
15
16 17 18
(6,4,5) (3,6,6) (5,5,5) (4,6,6) (6,5,5) (6,6,5) (6,6,6)
(6,5,4) (4,6,5) (4,5,6) (5,6,4) (5,4,6) (6,6,3) (6,3,6) (6,6,4) (6,4,6) (5,5,6) (5,6,5) (6,5,6) (5,6,6)
10/216 150/216 6/216
96/216
3/216 51/216 1/216 18/216 1 E(x)=10.5
สรุป ค่าความคาดหวังทางคณิตศาสตร์ของผลรวมของแต้มบนหน้าลูกเต๋า 3ลูกท่ีโยนพร้อมกัน 1ครัง้ เป็ น 10.5
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การออกแต้มท่ีเป็ นไปได้
(1,1,1) (1,1,2) (1,1,3) (1,1,4) (1,2,3) (2,2,2) (1,1,5) (1,2,4) (1,3,3) (2,2,3) (1,1,6) (1,2,5) (1,3,4) (3,2,3) (2,2,4) (1,2,6) (1,3,5) (1,4,4) (3,2,4) (2,2,5) (3,3,3) (1,3,6) (1,5,4) (2,2,6) (3,2,5) (2,4,4) (3,4,3) (1,4,6) (1,5,5) (3,2,6) (4,2,5) (3,5,3) (3,4,4) (1,5,6) (6,2,4) (3,6,3) (4,3,5) (2,5,5) (4,4,4) (1,6,6) (6,2,5) (6,3,4) (5,4,4) (3,5,5) (6,3,5) (2,6,6) (6,4,4) (4,5,5)
(1,2,1) (1,3,1) (1,4,1) (1,3,2)
(2,1,1) (3,1,1) (1,2,2) (2,1,2) (2,2,1) (4,1,1) (2,1,3) (2,3,1) (3,1,2) (3,2,1)
(1,5,1) (1,4,2) (3,1,3) (3,2,2) (1,6,1) (1,5,2) (1,4,3) (3,3,2) (4,2,2) (1,6,2) (1,5,3) (4,4,1) (3,4,2) (5,2,2)
(5,1,1) (2,1,4) (3,3,1) (2,3,2) (6,1,1) (2,1,5) (3,1,4) (2,3,3) (2,2,4) (2,1,6) (3,1,5) (4,1,4) (2,3,4) (2,5,2)
(1,6,3) (1,4,5) (6,2,2) (3,5,2) (4,4,2) (3,3,4) (1,6,4) (5,5,1) (3,6,2) (4,5,2) (3,3,5) (4,4,3) (1,6,5) (6,4,2) (3,3,6) (4,5,3) (5,5,2)
(3,1,6) (5,1,4) (2,2,6) (2,3,5) (4,2,4) (4,3,3) (4,1,6) (5,1,5) (2,3,6) (2,4,5) (5,3,3) (4,3,4) (5,1,6) (2,6,4) (6,3,3) (3,4,5) (5,2,5)
(6,6,1) (6,5,2) (6,4,3) (4,4,5) (5,5,3) (6,5,3) (6,6,2) (4,4,6) (5,5,4)
(6,1,6) (2,6,5) (2,5,6) (5,6,2) (5,2,6) (3,6,4) (3,4,6) (4,6,3) (4,3,6) (4,5,4) (5,3,5) (3,6,5) (3,5,6) (5,6,3) (5,3,6) (6,2,6) (4,6,4) (5,4,5)
P(x) 1/216 3/216 6/216
xP(x) 3/216 12/216 30/216
10/216
60/216
(2,4,1) (4,1,2) (4,2,1)
15/216 105/216
(2,5,1) (5,1,2) (5,2,1) (3,4,1) (4,1,3) (4,3,1)
21/216 168/216
(2,6,1) (6,1,2) (6,2,1) (3,5,1) (5,1,3) (5,3,1)
25/216 225/216
(2,4,3) (4,3,2) (4,2,3)
(3,6,1) (6,1,3) (6,3,1) (5,4,1) (4,1,5) (4,5,1) 27/216 270/216 (2,5,3) (5,3,2) (5,2,3)
(4,6,1) (6,1,4) (6,4,1) (2,6,3) (6,3,2) (6,2,3) (2,5,4) (5,4,2) (5,2,4)
27/216 297/216
(5,6,1) (6,1,5) (6,5,1) (2,4,6) (4,6,2) (4,2,6) 25/216 300/216 (3,5,4) (5,4,3) (5,3,4)
21/216 273/216
15/216 210/216
15
16 17 18
(6,4,5) (3,6,6) (5,5,5) (4,6,6) (6,5,5) (6,6,5) (6,6,6)
(6,5,4) (4,6,5) (4,5,6) (5,6,4) (5,4,6) (6,6,3) (6,3,6) (6,6,4) (6,4,6) (5,5,6) (5,6,5) (6,5,6) (5,6,6)
10/216 150/216 6/216
96/216
3/216 51/216 1/216 18/216 1 E(x)=10.5
สรุป ค่าความคาดหวังทางคณิตศาสตร์ของผลรวมของแต้มบนหน้าลูกเต๋า 3ลูกท่ีโยนพร้อมกัน 1ครัง้ เป็ น 10.5
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