## Pure guessing

Forum for the GRE subject test in mathematics.
Jenn
Posts: 10
Joined: Tue Nov 20, 2012 5:09 am

### Pure guessing

Probably somebody have done this before but I have counted probabilities of making score worse by pure guessing (all expectations are evidently zero).
It seems that it's strongly recommended to guess on =4(mod 5) questions.
It's better to guess on =0(mod 5) questions but there is a huge probability of not changing the score at all.

Number of questions to be guessed Probability of worsening of the score
1 0.800
2 0.640
3 0.512
4 0.410
5 0.328
6 0.655
7 0.577
8 0.503
9 0.436
10 0.376
11 0.617
12 0.558
13 0.502
14 0.448
15 0.398
16 0.598
17 0.549
18 0.501
19 0.455
20 0.411
21 0.586
22 0.543
23 0.501
24 0.460
25 0.421
26 0.577
27 0.539
28 0.501
29 0.463
30 0.428
31 0.571
32 0.535
33 0.500
34 0.466
35 0.433
36 0.566
37 0.533
38 0.500
39 0.468
40 0.437

IIIII
Posts: 71
Joined: Sun Nov 11, 2012 7:33 pm

### Re: Pure guessing

Jenn wrote:Probably somebody have done this before but I have counted probabilities of making score worse by pure guessing (all expectations are evidently zero).
It seems that it's strongly recommended to guess on =4(mod 5) questions.
The key here is that the expected value is 0 for any guess. It is true that the majority of "=4(mod 5) guesses" will have a positive outcome. Yet, the magnitude of the negative guesses is on average higher. So, it is unwise to recommend guessing, (unless you consider something like Score Select, or you otherwise do not have a risk averse utility function.).