$M$

$T$

$\overline{T}$

$\overline{T}$

$T$

$\overline{M}$

Résultats

Calculs intermédiaires

P(M)

P_M(T)

P_{\overline M} \left(\, \overline T \,\right )

1

1

P(M\cap \overline{T})

P(M\cap T)

P(\overline{M}\cap T)

P(\overline{M}\cap \overline{T})

r(x) = (x^(2) * (3 - (2 * x)))
M = (-5.860811836631652, 3.2674882132037966)
A = (-7.848834571048115, 2.028612883485791)
f = Segment(A, M)
D = Point(f)
n = Segment(A, D)
g = OrthogonalLine(A, yAxis)
C = (-3.6070782811642084, 3.8751485268903254)
h = Segment(M, C)
i = OrthogonalLine(M, yAxis)
C' = Mirror(C, i)
C'_1 = Mirror(C, g)
C'' = Mirror(C', g)
B' = Mirror(M, g)
j = Segment(A, B')
k = Segment(B', C'')
l = Segment(B', C'_1)
p1: r(n / f)
m = Segment(M, C')
text1: "P(M)=" + (LaTeX[p1]) + ""
p1': 1 - p1
text2: "" + p1' + ""
E = Point(h)
F = Point(l)
p = Segment(M, E)
p2: r(p / h)
q = Segment(B', F)
p3: r(q / h)
text4: "P_{\overline M} \left(\, \overline T \,\right )=" + (LaTeX[p3]) + ""
text3: "P_M(T)=" + (LaTeX[p2]) + ""
p2': 1 - p2
p3': 1 - p3
text5: "" + p2' + ""
text6: "" + p3' + ""
PT: (p1 * p2) + (p1' * p3')
PMT: (p1 * p2 / PT)
texte5: "\text{La probabilité que le test soit positif est :}\\
P(T)=P(M\cap T)+P(\overline{M}\cap T)\approx" + (LaTeX[PT]) + ""
text7: "\text{La probabilité d'être malade}\\ 
\text{sachant que le test est positif est :}\\
P_T(M)=\frac{P(M\cap T)}{P(T)}\approx" + (LaTeX[PMT]) + ""
a = false
b = false
B = Intersect(xAxis, yAxis)
G = (4, 0)
poly1, s, t, c, d, H, I = Polygon(B, G, 4)
J: B + (p1' * (I - B))
K: I + (p2 * (H - I))
L: B + (p3' * (G - B))
e = OrthogonalLine(K, c)
f_1 = OrthogonalLine(J, d)
g_1 = OrthogonalLine(L, s)
N = Intersect(e, f_1)
O = Intersect(f_1, g_1)
q1, j_1, n_1, k_1, i_1 = Polygon(J, N, K, I)
P = Intersect(f_1, t)
q2, i_2, j_2, p_1, h_1 = Polygon(I, J, P, H)
q3, l_1, g_2, p_2, o = Polygon(L, G, P, O)
q4, b_1, l_2, o_1, j_3 = Polygon(B, L, O, J)
q5, k_2, n_2, p_3, h_2 = Polygon(K, N, P, H)
R = Midpoint(i_2)
u = 0.46 (slider from 0 to 0.5, step 0.01)
Q: I + (0, u)
S: K + (0, u)
T = Midpoint(Q, S)
v = Vector(Q, S)
w = Vector(S, Q)
U: L - (0, u)
V: G - (0, u)
u_1 = Vector(U, V)
v_1 = Vector(V, U)
W = Midpoint(U, V)
Z: H + ((2 * u), 0)
A_1: G + ((2 * u), 0)
B_1 = Midpoint(A_1, Z)
C_1: I + (0, (2 * u))
D_1: H + (0, (2 * u))
E_1 = Midpoint(C_1, D_1)
w_1 = Vector(C_1, D_1)
a_1 = Vector(D_1, C_1)
c_1 = Vector(Z, A_1)
d_1 = Vector(A_1, Z)
F_1 = Centroid(q1)
G_1 = Centroid(q5)
H_1 = Centroid(q3)
I_1 = Centroid(q4)
J_1 = (-1.2741229467592718, 3.9677460381556053)
e_1 = Vector(J_1, F_1)
K_1 = (-1.2040971621810674, 2.4505207507600195)
m_1 = Vector(K_1, G_1)
L_1 = (-1.1807552339883338, -0.05873645531729537)
q_1 = Vector(L_1, H_1)
M_1 = (-1.215768126277436, 1.5285146145734712)
r_1 = Vector(M_1, I_1)
s_1 = Segment(O, L)
t_1 = Segment(N, K)
polhach1, j_4, n_3, k_3, i_3 = Polygon(J, N, K, I)
polhach2, b_2, l_3, o_2, j_5 = Polygon(B, L, O, J)