probability

Matrix

Member
Dear all,

Where can I find the probability of sets?

For example, the probability of 2nd number, 3rd number, 4th number and 5th number.

01=1st===>0.142857 (lotto 6/42)

02=1st===>0.125436

03=1st===>0.109756
----------
25=1st===>0.001180

GillesD

Member
Probability for sets

If you use Excel, you can calculate the values you are looking for with the formula: =COMBIN(42-N,5)/COMBIN(42,6)

Replace N by the position you are looking for.

For example, with the above formula, COMBIN(42-1,5) will give 0.142857143 and COMBIN(42-25,5) will give 0.001179614.

The COMBIN(42-N,5) gives you the remaining number of combinations when N is the first position.

Matrix

Member
2nd Expected
1 0
2 0.017421603
3 0.031358885
4 0.042213884
5 0.050360423
6 0.056145
7 0.059888
8 0.0618843
9 0.062404
10 0.061695
11 0.059981
12 0.057466
13 0.054331
14 0.049057
15 0.0468375
16 0.0427485
17 0.03858
18 0.0344356
19 0.030384
20 0.02649459
21 0.022818
22 0.019395568
23 0.0162553
24 0.01341648
25 0.010888
26 0.008674
27 0.006765
28 0.005152
29 0.003816
30 0.002736
31
32
33
34
35
36
37
38
==========

3rd Expected
1 0
2 0
3 0.00174216
4 0.004824
5 0.008887
6 0.0136109
7 0.018715
8 0.023955
9 0.029122
10 0.0340387
11 0.0385595
12 0.0425675
13 0.0459729
14 0.04871109
15 0.0507407
16 0.0520417
17 0.0526136
18 0.0524335
19 0.05165346
20 0.050200294
21 0.048171999
22 0.045636631
23 0.042670249
24 0.039355
25 0.035777288
26 0.0320257
27 0.02818929
28 0.02435554
29 0.02060854
30 0.017027
31 0.0136824
32 0.0106371
33 0.0079423
34 0.00563652
35 0.003743
36 0.002268488
37 0.001200964
38 0.0005078

======
4th Expected
42 0
41 0
40 0.00174216
39 0.004824
38 0.008887
37 0.0136109
36 0.018715
35 0.023955
34 0.029122
33 0.0340387
32 0.0385595
31 0.0425675
30 0.0459729
29 0.04871109
28 0.0507407
27 0.0520417
26 0.0526136
25 0.0524335
24 0.05165346
23 0.050200294
22 0.048171999
21 0.045636631
20 0.042670249
19 0.039355
18 0.035777288
17 0.0320257
16 0.02818929
15 0.02435554
14 0.02060854
13 0.017027
12 0.0136824
11 0.0106371
10 0.0079423
9 0.00563652
8 0.003743
7 0.002268488
6 0.001200964
5 0.0005078
=======
5th Expected
42 0
41 0.017421603
40 0.031358885
39 0.042213884
38 0.050360423
37 0.056145
36 0.059888
35 0.0618843
34 0.062404
33 0.061695
32 0.059981
31 0.057466
30 0.054331
29 0.049057
28 0.0468375
27 0.0427485
26 0.03858
25 0.0344356
24 0.030384
23 0.02649459
22 0.022818
21 0.019395568
20 0.0162553
19 0.01341648
18 0.010888
17 0.008674
16 0.006765
15 0.005152
14 0.003816
13 0.002736
12
11
10
9
8
7
6
5
========
Thanks for GillesD,PAB

GillesD

Member
Probabilities

To get the proper probability for number X in position Y for a 6/42 lottery, it might be easier to remember the following Excel formula:

=COMBIN(X-1,Y-1)*COMBIN(42-X,6-Y)/COMBIN(42,6)

where the first COMBIN function gives the number of possible combinations before number X in position Y, the second COMBIN function gives the number of possible combinations after number X in position Y and the last COMBIN function gives the number of possible combinations for a 6 / 42 lottery.

So for number #12 in position #3, this gives =COMBIN(12-1,3-1)*COMBIN(42-12,6-3)/COMBIN(42,6) or 0.042567501

Matrix

Member
Thanks again, GillesD.