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Remove["Global`*"]

1.

p = 2/6 * 2/36 * 1/6

N[%]

2.

p1 =  97/213

N[%]

p1 =  97/148

N[%]

3.

a

f[t_] := 22 + 16 t + 3 (t^2);
g[t_] := 21 + 10 t + (t^2)

Plot[{f[t], g[t]}, {t, 0, 4}];

Limit[g[t]/f[t], t -> Infinity]

b

f[t_] := 2 E^t;
g[t_] := 1/2 E^(t/2);

Plot[{f[t], g[t]}, {t, 0, 4}];

Limit[g[t]/f[t], t -> Infinity]

c

p = 289/1000

N[%]

4.

a

r1g2 = 4/10* 3/9;
g1r2 = 2/10* 4/9;
r1g2 + g1r2

N[%]

b

3!

r = 4; j = 2; v = 3; n = 1;

r1j2v3 = r*j*v /(10*9*8)    ;
r1v2j3 = r*v*j /(10*9*8)  ;
r1j2v3 == r1v2j3

nF = r*v*j /(10*9*8)   ;
vF = r*n*j /(10*9*8)   ;
jF = r*n*v /(10*9*8)   ;
nF = r*j*v /(10*9*8)   ;

p = 6 (nF + vF + jF + nF)

N[%]

5.  Treppenfunktion

Remove["Global`*"]

h[x_] := Sign[(Sign[x] + 1)/2];
p[1] = 1/6; t[1] = 0;
p[2] = 1/3; t[2] = 2;
p[3] = 1/12; t[3] = 3;
p[4] = 1/12; t[4] = 5;
p[5] = 1/3; t[5] = 7;
F[x_] := Sum[p[k] h[x - t[k]], {k, 1, 5}]

F[x]

Plot[F[x], {x, -2, 9}];

Table[{t[k], F[t[k]]}, {k, 1, 5}] // N // TableForm