Author: Φεργαδιώτης Αθανάσιος ,Καστανιώτης Δημήτριος

25

50

75

100

f %

Πραγματική

Θεωρητική πιθανότητα

Tιμές
  x_i

Συχνότητα
      ν_i

       Σχετική
Συχνότητα f_i %

Φεργαδιώτης Αθανάσιος - Καστανιώτης Δημήτριος

Σωστά !!! Συγχαρητήρια !!!

Πατήστε το κουμπί  ''Eπόμενο'' στο κάτω μέρος της εφαρμογής

Κερδίσατε !!!

Xάσατε !!!

D_1 = (14.079573863636364, -4.7290369318181815)
F_1: D_1 + (0.0, 5.0)
z = Vector(D_1, F_1)
n = OrthogonalLine(F_1, z)
E_1: D_1 + (3.9, 0.0)
l = Segment(D_1, E_1)
M_1 = Point(l)
w = Vector(D_1, E_1)
q = OrthogonalLine(M_1, w)
P_1 = Intersect(q, n)
dik = 8 (slider from 2 to 12, step 1)
ok2 = If(dik ≟ 2.0, 0.9722222222222222, If[dik ≟ 3.0, 0.9166666666666666, If[dik ≟ 4.0, 0.8333333333333334, If[dik ≟ 5.0, 0.7222222222222222, If[dik ≟ 6.0, 0.5833333333333334, If[dik ≟ 7.0, 0.4166666666666667, If[dik ≟ 8.0, 0.2777777777777778, If[dik ≟ 9.0, 0.16666666666666666, If[dik ≟ 10.0, 0.08333333333333333, If[dik ≟ 11.0, 0.027777777777777776, If[dik ≟ 12.0, 0.0]]]]]]]]]])
pik = If(dik ≟ 2.0, 0.03, If[dik ≟ 3.0, 0.05, If[dik ≟ 4.0, 0.08, If[dik ≟ 5.0, 0.1, If[dik ≟ 6.0, 0.5, If[dik ≟ 7.0, 0.8, If[dik ≟ 8.0, 2.0, If[dik ≟ 9.0, 5.0, If[dik ≟ 10.0, 7.0, If[dik ≟ 11.0, 25.0]]]]]]]]])
B1 = Random(1.0, 6.0)
A1 = Random(1.0, 6.0)
D1: A1 + B1
B2 = Random(1.0, 6.0)
A2 = Random(1.0, 6.0)
D2: A2 + B2
F2 = If(D2 < dik + 1.0, -1.0, pik)
F1 = If(D1 < dik + 1.0, -1.0, pik)
G2: F1 + F2
t = 0 (slider from 0 to 1, step 0.0333)
A30 = Random(1.0, 6.0)
A29 = Random(1.0, 6.0)
A28 = Random(1.0, 6.0)
A27 = Random(1.0, 6.0)
A26 = Random(1.0, 6.0)
A25 = Random(1.0, 6.0)
A24 = Random(1.0, 6.0)
A23 = Random(1.0, 6.0)
A22 = Random(1.0, 6.0)
A21 = Random(1.0, 6.0)
A20 = Random(1.0, 6.0)
A19 = Random(1.0, 6.0)
A18 = Random(1.0, 6.0)
A17 = Random(1.0, 6.0)
A16 = Random(1.0, 6.0)
A15 = Random(1.0, 6.0)
A14 = Random(1.0, 6.0)
A13 = Random(1.0, 6.0)
A12 = Random(1.0, 6.0)
A11 = Random(1.0, 6.0)
A10 = Random(1.0, 6.0)
A9 = Random(1.0, 6.0)
A8 = Random(1.0, 6.0)
A7 = Random(1.0, 6.0)
A6 = Random(1.0, 6.0)
A5 = Random(1.0, 6.0)
A4 = Random(1.0, 6.0)
A3 = Random(1.0, 6.0)
a1 = 30
a: ceil(a1 * t)
B3 = Random(1.0, 6.0)
D3: A3 + B3
B4 = Random(1.0, 6.0)
D4: A4 + B4
B5 = Random(1.0, 6.0)
D5: A5 + B5
B6 = Random(1.0, 6.0)
D6: A6 + B6
B7 = Random(1.0, 6.0)
D7: A7 + B7
B8 = Random(1.0, 6.0)
D8: A8 + B8
B9 = Random(1.0, 6.0)
D9: A9 + B9
B10 = Random(1.0, 6.0)
D10: A10 + B10
B11 = Random(1.0, 6.0)
D11: A11 + B11
B12 = Random(1.0, 6.0)
D12: A12 + B12
B13 = Random(1.0, 6.0)
D13: A13 + B13
B14 = Random(1.0, 6.0)
D14: A14 + B14
B15 = Random(1.0, 6.0)
D15: A15 + B15
B16 = Random(1.0, 6.0)
D16: A16 + B16
B17 = Random(1.0, 6.0)
D17: A17 + B17
B18 = Random(1.0, 6.0)
D18: A18 + B18
B19 = Random(1.0, 6.0)
D19: A19 + B19
B20 = Random(1.0, 6.0)
D20: A20 + B20
B21 = Random(1.0, 6.0)
D21: A21 + B21
B22 = Random(1.0, 6.0)
D22: A22 + B22
B23 = Random(1.0, 6.0)
D23: A23 + B23
B24 = Random(1.0, 6.0)
D24: A24 + B24
B25 = Random(1.0, 6.0)
D25: A25 + B25
B26 = Random(1.0, 6.0)
D26: A26 + B26
B27 = Random(1.0, 6.0)
D27: A27 + B27
B28 = Random(1.0, 6.0)
D28: A28 + B28
B29 = Random(1.0, 6.0)
D29: A29 + B29
B30 = Random(1.0, 6.0)
D30: A30 + B30
L_S: {D1, D2, D3, D4, D5, D6, D7, D8, D9, D10, D11, D12, D13, D14, D15, D16, D17, D18, D19, D20, D21, D22, D23, D24, D25, D26, D27, D28, D29, D30}
Lss = Sequence(Element[L_S, k], k, 1.0, a, 1.0)
Lss2 = KeepIf(x ≤ dik, Lss)
Lss1 = KeepIf(x > dik, Lss)
J_1 = Point(l)
p = OrthogonalLine(J_1, w)
O_1 = Intersect(p, n)
mΩss = Length(Lss1)
Ωs7 = KeepIf(x ≤ dik, L_S)
mΩs7 = Length(Ωs7)
Ωs8 = KeepIf(x > dik + 1.0, L_S)
mΩs8 = Length(Ωs8)
mΩs: mΩs7 + mΩs8
L_B: {B1, B2, B3, B4, B5, B6, B7, B8, B9, B10, B11, B12, B13, B14, B15, B16, B17, B18, B19, B20, B21, B22, B23, B24, B25, B26, B27, B28, B29, B30}
A4000 = Random(1.0, 2.0)
A3999 = Random(1.0, 2.0)
A3998 = Random(1.0, 2.0)
A3997 = Random(1.0, 2.0)
A3996 = Random(1.0, 2.0)
A3995 = Random(1.0, 2.0)
A3994 = Random(1.0, 2.0)
A3993 = Random(1.0, 2.0)
A3992 = Random(1.0, 2.0)
A3991 = Random(1.0, 2.0)
A3990 = Random(1.0, 2.0)
A3989 = Random(1.0, 2.0)
A3988 = Random(1.0, 2.0)
A3987 = Random(1.0, 2.0)
A3986 = Random(1.0, 2.0)
A3985 = Random(1.0, 2.0)
A3984 = Random(1.0, 2.0)
A3983 = Random(1.0, 2.0)
A3982 = Random(1.0, 2.0)
L_A: {A1, A2, A3, A4, A5, A6, A7, A8, A9, A10, A11, A12, A13, A14, A15, A16, A17, A18, A19, A20, A21, A22, A23, A24, A25, A26, A27, A28, A29, A30}
L_2 = Sequence(Element[L_A, k], k, 1.0, a, 1.0)
A = (-3.3763636363636347, -1.5698181818181818)
a_1 = OrthogonalLine(A, yAxis)
B = Point(a_1)
c = OrthogonalLine(A, a_1)
ΩΤ1 = Sequence(If[Element[L_2, κ] ≟ 1.0, "Κ", "Γ"], κ, 1.0, a, 1.0)
E: A + a / a1 * (B - A)
u1: ceil(a1 / 2.0)
u2: ceil(a1 / 4.0)
u3: ceil(3.0 * a1 / 4.0)
P = Point(c)
Q = Point(a_1)
R = (7.620198863636364, -3.7104431818181816)
U = (-3.981832386363635, 4.637056818181818)
V = (18.178792613636364, 3.1961193181818177)
πολύγ.1 = Τετράπλευρογιακείμενο(U, V)
W = (-3.932144886363635, -3.3626306818181817)
La2 = RemoveUndefined(Sequence[Element[L_A, k], k, 11.0, If[a > 20.0, 20.0, a], 1.0])
La1 = RemoveUndefined(Sequence[Element[L_A, k], k, 1.0, If[a > 10.0, 10.0, a], 1.0])
La3 = RemoveUndefined(Sequence[Element[L_A, k], k, 21.0, If[a > 30.0, 30.0, a], 1.0])
Mx = Sequence(ι, ι, 1.0, a, 1.0)
N1 = RemoveUndefined(Sequence[Element[Mx, k], k, 1.0, If[a > 10.0, 10.0, a], 1.0])
N2 = RemoveUndefined(Sequence[Element[Mx, k], k, 11.0, If[a > 20.0, 20.0, a], 1.0])
N3 = RemoveUndefined(Sequence[Element[Mx, k], k, 21.0, If[a > 30.0, 30.0, a], 1.0])
κείμενο20 = TableText({N2}, "vl")
κείμενο21 = TableText({N3}, "vl")
κείμενο18 = TableText({N1}, "vr")
B_1 = (-3.9763636363636343, -1.6898181818181817)
C_1 = (6.903636363636364, -4.709818181818181)
ΩΤ11: {}
κείμενο26: "Aριθμός\,\,ρίψεων\,:\,\,\,\fgcolor{ae0000}{" + a + "}"
m = Segment(D_1, F_1)
G_1 = Midpoint(m)
H_1: (D_1 + G_1) / 2.0
I_1: (F_1 + G_1) / 2.0
K_1 = Point(l)
N_1 = Point(l)
Q_1: J_1 + Length[Lss1] / (Length[Lss2] + Length[Lss1]) * (O_1 - J_1)
R_1: (x(K_1), y(Q_1))
S_1: M_1 + ok2 * (P_1 - M_1)
T_1: (x(N_1), y(S_1))
πολύγ.3, j_1, q_1, r_1, k_1 = Polygon(J_1, Q_1, R_1, K_1)
πολύγ.4, m_1, s_1, t_1, n_1 = Polygon(M_1, S_1, T_1, N_1)
U_1 = (15.396292613636364, 2.2769005681818175)
V_1: U_1 + (1.5, 0.0)
W_1: U_1 - (0.0, 0.5)
Z_1: W_1 + (1.5, 0.0)
k = Segment(U_1, V_1)
r = Segment(W_1, Z_1)
A_2 = (6.452542613636364, 1.9290880681818177)
B_2 = (8.042542613636364, 1.0595568181818178)
πολύγ.5 = Τετράπλευρογιακείμενο(A_2, B_2)
C_2 = (8.166761363636365, 1.9290880681818177)
D_2 = (10.129417613636363, 1.0595568181818178)
πολύγ.6 = Τετράπλευρογιακείμενο(C_2, D_2)
E_2 = (10.278480113636364, 1.9290880681818177)
F_2 = (12.489573863636364, 1.0595568181818178)
πολύγ.7 = Τετράπλευρογιακείμενο(E_2, F_2)
G_2 = (6.477386363636364, 0.9353380681818179)
H_2 = (8.067386363636365, -0.20747443181818204)
πολύγ.8 = Τετράπλευρογιακείμενο(G_2, H_2)
I_2 = (8.216448863636364, -0.356536931818182)
J_2 = (10.179105113636364, -0.803724431818182)
πολύγ.9 = Τετράπλευρογιακείμενο(I_2, J_2)
K_2 = (10.346136363636365, -0.3720056818181818)
M_2 = (12.539261363636363, -0.803724431818182)
πολύγ.10 = Τετράπλευρογιακείμενο(K_2, M_2)
N_2 = (8.191605113636363, 0.9353380681818179)
O_2 = (10.154261363636364, -0.20747443181818204)
πολύγ.11 = Τετράπλευρογιακείμενο(N_2, O_2)
P_2 = (10.326136363636362, 0.9261193181818177)
Q_2 = (12.514417613636363, -0.20747443181818204)
πολύγ.12 = Τετράπλευρογιακείμενο(P_2, Q_2)
R_2 = (-3.9963636363636343, 3.4901818181818176)
S_2 = (3.4636363636363643, -2.3098181818181818)
T_2 = (3.6036363636363644, 3.4901818181818176)
U_2 = (9.683636363636364, 0.090181818181818)
V_2 = (3.6036363636363644, -0.10981818181818197)
W_2 = (9.663636363636364, -2.3098181818181818)
Z_2 = (-3.9163636363636325, -4.062786931818183)
A_3 = (6.104730113636364, -5.151380681818182)
πολύγ.16 = Τετράπλευρογιακείμενο(Z_2, A_3)
B_3 = (-3.9963636363636343, -3.1898181818181817)
C_3 = (13.423636363636362, -4.549818181818181)
f = true
ok1 = -1
Lb1 = RemoveUndefined(Sequence[Element[L_B, k], k, 1.0, If[a > 10.0, 10.0, a], 1.0])
Lb2 = RemoveUndefined(Sequence[Element[L_B, k], k, 11.0, If[a > 20.0, 20.0, a], 1.0])
Lb3 = RemoveUndefined(Sequence[Element[L_B, k], k, 21.0, If[a > 30.0, 30.0, a], 1.0])
Lab1 = RemoveUndefined(Sequence["(" + (Element[L_A, k]) + "," + (Element[L_B, k]) + ")...." + (Element[L_S, k]), k, 1.0, If[a > 10.0, 10.0, a], 1.0])
κείμενο15 = TableText({Lab1}, "vl")
Lab2 = RemoveUndefined(Sequence["(" + (Element[L_A, k]) + "," + (Element[L_B, k]) + ")...." + (Element[L_S, k]), k, 11.0, If[a > 20.0, 20.0, a], 1.0])
κείμενο16 = TableText({Lab2}, "vl")
Lab3 = RemoveUndefined(Sequence["(" + (Element[L_A, k]) + "," + (Element[L_B, k]) + ")...." + (Element[L_S, k]), k, 21.0, If[a > 30.0, 30.0, a], 1.0])
κείμενο17 = TableText({Lab3}, "vl")
κείμενο6: (mΩs8 + mΩs7) / mΩs * 100.0 + ""
F3 = If(D3 < dik + 1.0, -1.0, pik)
F4 = If(D4 < dik + 1.0, -1.0, pik)
F5 = If(D5 < dik + 1.0, -1.0, pik)
F6 = If(D6 < dik + 1.0, -1.0, pik)
F7 = If(D7 < dik + 1.0, -1.0, pik)
F8 = If(D8 < dik + 1.0, -1.0, pik)
F9 = If(D9 < dik + 1.0, -1.0, pik)
F10 = If(D10 < dik + 1.0, -1.0, pik)
F11 = If(D11 < dik + 1.0, -1.0, pik)
F12 = If(D12 < dik + 1.0, -1.0, pik)
F13 = If(D13 < dik + 1.0, -1.0, pik)
F14 = If(D14 < dik + 1.0, -1.0, pik)
F15 = If(D15 < dik + 1.0, -1.0, pik)
F16 = If(D16 < dik + 1.0, -1.0, pik)
F17 = If(D17 < dik + 1.0, -1.0, pik)
F18 = If(D18 < dik + 1.0, -1.0, pik)
F19 = If(D19 < dik + 1.0, -1.0, pik)
F20 = If(D20 < dik + 1.0, -1.0, pik)
F21 = If(D21 < dik + 1.0, -1.0, pik)
F22 = If(D22 < dik + 1.0, -1.0, pik)
F23 = If(D23 < dik + 1.0, -1.0, pik)
F24 = If(D24 < dik + 1.0, -1.0, pik)
F25 = If(D25 < dik + 1.0, -1.0, pik)
F26 = If(D26 < dik + 1.0, -1.0, pik)
F27 = If(D27 < dik + 1.0, -1.0, pik)
F28 = If(D28 < dik + 1.0, -1.0, pik)
F29 = If(D29 < dik + 1.0, -1.0, pik)
F30 = If(D30 < dik + 1.0, -1.0, pik)
G3: G2 + F3
G4: G3 + F4
G5: G4 + F5
G6: G5 + F6
G7: G6 + F7
G8: G7 + F8
G9: G8 + F9
G10: G9 + F10
G11: G10 + F11
G12: G11 + F12
G13: G12 + F13
G14: G13 + F14
G15: G14 + F15
G16: G15 + F16
G17: G16 + F17
G18: G17 + F18
G19: G18 + F19
G20: G19 + F20
G21: G20 + F21
G22: G21 + F22
G23: G22 + F23
G24: G23 + F24
G25: G24 + F25
G26: G25 + F26
G27: G26 + F27
G28: G27 + F28
G29: G28 + F29
G30: G29 + F30
G1: F1
L_K: {G1, G2, G3, G4, G5, G6, G7, G8, G9, G10, G11, G12, G13, G14, G15, G16, G17, G18, G19, G20, G21, G22, G23, G24, G25, G26, G27, G28, G29, G30}
kerdos = Element(L_K, a)
κείμενο8: "Μέχρι τώρα " + (If[Element[L_K, a] > 0.0, "κερδίζετε  ", If[Element[L_K, a] ≟ 0.0, "ούτε κερδίζετε ούτε χάνετε", "χάνετε "]]) + (If[Element[L_K, a] ≠ 0.0, abs(Element[L_K, a]) + "€", ""])
κείμενο4: Length[Lss2] + ""
κείμενο5: Length[Lss1] + ""
κείμενο3: Length[Lss2] + Length[Lss1] + ""
κείμενο33: Length[Lss2] / (Length[Lss2] + Length[Lss1]) * 100.0 + ""
κείμενο32: Length[Lss1] / (Length[Lss2] + Length[Lss1]) * 100.0 + ""
κείμενο7: Length[Lss1] / (Length[Lss2] + Length[Lss1]) * 100.0 + ""
C = (10.030042613636363, -3.685599431818182)
G = (6.551917613636364, -1.424818181818182)
H = (12.564105113636364, -5.151380681818182)
πολύγ.2 = Τετράπλευρογιακείμενο(G, H)
κείμενο11: "\fgcolor{00ae00}{" + (Element[L_A, a]) + "} \,\,+\,\, \fgcolor{a60000}{" + (Element[L_B, a]) + "}\,\,\, =\,\,\, " + (Element[L_S, a])
κείμενο9: ok2 * 100.0 + "%"
κείμενο49 = If(ok1 ≟ -1.0, "", If[ok1 ≠ ok2, "Απαντήσατε λάθος !!!  Προσπαθείστε περισσότερο !!!"])
m5 = 5
κείμενο46: "1- " + dik
κείμενο2: dik + 1.0 + " - 12"
κείμενο10: "\begin{array}Aπόκλιση:\,\,  \\ " + " \,\,\,\,\,\," + ((Length[Lss1] / (Length[Lss2] + Length[Lss1]) - ok2) * 100.0) + "  %"
κείμενο37: "Στην\,\, " + a + "\,\, ρίψη \,,\, φέρατε \,\,άθροισμα\,\, ενδείξεων\,\,  " + (Element[L_S, a]) + ".      " + (If[Element[L_S, a] > dik, "\,\,\,\,\fgcolor{00ae00}{Κερδίσατε \,\," + pik + "€ }", "\fgcolor{aa0000}{\,\,\,Xάσατε \,\,1€ }"])
D: C + (1.7, 0.0)
F: C + (0.0, 1.7)
S: R + (1.7, 0.0)
T: R + (0.0, 1.7)
A_1: W + (0.0, 5.64)
Z: W + (10.0, 0.0)
U1: "\begin{array}\mbox{Θα ρίξουμε δύο  ζάρια μέχρι 30 φορές .Αν το άθροισμα των ενδείξεων των ζαριών σε κάποια ρίψη είναι μεγαλύτερο από}\,\,\fgcolor{ae0000}{" + dik + "}\,\, κερδίζουμε\,\," + pik + "€\\ 
ειδάλλως\,\, χάνουμε \,\,1 \,\,ευρώ.\,\, Ποιά\,\, η\,\, πιθανότητα\,\, να\,\, φέρουμε\,\, στη\,\, ρίψη \,\,δύο\,\, ζαριών\,\, άθροισμα\,\, ενδείξεων\,\, μεγαλύτερη \,\,του\,\, \fgcolor{ae0000}{" + dik + "};\\Γράψτε \,\,την\,\, πιθανότητα\,\, στο\,\, κάτω\,\, μέρος\,\, της\,\, εφαρμογής\,\, για\,\, να\,\, αρχίσει\,\, το\,\, παιχνίδι"

Tool: Τετράπλευρο για κείμενο (command Τετράπλευρογιακείμενο)
Σημείο , Σημείο
Input: A, B
Output: πολύγ1

a = OrthogonalLine(A, yAxis)
b = OrthogonalLine(A, a)
c = OrthogonalLine(B, a)
d = OrthogonalLine(B, b)
C = Intersect(b, d)
D = Intersect(c, a)
πολύγ1, a_1, d_1, b_1, c_1 = Polygon(A, D, B, C)

Tool: Διαίρεση Τμήματος Σε Ισα μέρη (command ΔιαίρεσηΤμήματοςΣεΙσαμέρη)
Σημείο , Σημείο, Αριθμός
Input: A, B, n
Output: λίστα1

λίστα1 = Sequence(A + j * (B - A) / n, j, 1.0, n, 1.0)