I don't have access to Mathematica right now will ListLinePlot give a similar result as the figure above

S M Blinder, I don't think you've got my question I'll write my program for your assistance

f[x_] :=1- 365!/((365-x)!*365^x).   

This program would give the chances for 'x' number of days. This made a table for all probabilities

In[2]:t=Table[1- 365!/((365-x)!*365^x),{x,1,366}].  
out[2]:{0,.......(all the probabilities ) ......,1}
In[3]: Plot[t]

The output instead of what shown in the shot above, showed some random lines What I expected that the first expr I.e.0 in out[2] would have 0 as y coordinate and 1 as x coordinate and the last value would have 1 as y coordinate and 366 as x The above figure shows till 100 but I wanted to expand it till 366

Or I suppose if I write Plot[Do[Print[n," ",N[P2[n,365]]],{n,1,366}]] it'd plot the above figure ?

Is this what you want? Set d=366 to include possible Feb 29. Table example goes to n=23, can expand to 366.

In[1]:= P2[n_, d_] := 1 - d!/((d - n)! d^n)

In[2]:= P2[23, 366] // N

Out[2]= 0.506323

In[3]:= Do[Print[n, "    ", N[P2[n, 366]]], {n, 1, 23}]

1    0.

2    0.00273224

3    0.00818179

4    0.0163114

5    0.0270621

6    0.0403536

7    0.0560856

8    0.0741386

9    0.094376

10    0.116645

11    0.140781

12    0.166604

13    0.193929

14    0.22256

15    0.252298

16    0.282941

17    0.314288

18    0.346138

19    0.378295

20    0.41057

21    0.442779

22    0.474751

23    0.506323