Here is a table that I created (based on an old posting). Basically, it is trying to predict the probability of passing based on questions you think you are worked out correctly. To be conservative, I am assuming that 75% of those are correct. Also, inside the table, I assumed that 25% of the questions guessed are correct. However the caveat is, don't depend on statistics too much, the recent polls are a prime example. Sorry for the tongue and cheek comment, but it serves as a good reminder.
Let me take an example,
42
32
13
1
87.33%
If you answered 42 questions, then 75% of them being correct is 32. As the passing grade is 60%, you need 33 (=55*0.6) questions to be correct. So, just one question out of the 13 you guessed needs to be correct. The probability is based on Binomial Distribution and is trying to predict basically what is the probability that you got one correct out of the 13 guessed, assuming the 1/4 chance to be correct. At least that is how I understood how the initial formula was set up from which I used as the basis of this table.
Please let me know if something is wrong and I will try to look at it more carefully.
I hope this is self explanatory.
t=
total number of questions
n=
number of questions you think you answered correctly
m=
fraction of "n" that were really correct (m=0.75 is a starting guess)
x=
number of questions answered correctly
y=
the number of questions guessed (t-n)
z=
number of questions that must be guessed correctly for passing
p=
percentage needed to pass
t=
55
m=
0.75
p=
60%
x
y
z
Probability of Passing
0
0
55
33
0.00%
1
1
54
32
0.00%
2
2
53
31
0.00%
3
2
52
31
0.00%
4
3
51
30
0.00%
5
4
50
29
0.00%
6
5
49
28
0.00%
7
5
48
28
0.00%
8
6
47
27
0.00%
9
7
46
26
0.00%
10
8
45
25
0.00%
11
8
44
25
0.00%
12
9
43
24
0.00%
13
10
42
23
0.00%
14
11
41
22
0.00%
15
11
40
22
0.00%
16
12
39
21
0.00%
17
13
38
20
0.01%
18
14
37
19
0.01%
19
14
36
19
0.01%
20
15
35
18
0.02%
21
16
34
17
0.04%
22
17
33
16
0.10%
23
17
32
16
0.06%
24
18
31
15
0.13%
25
19
30
14
0.27%
26
20
29
13
0.56%
27
20
28
13
0.38%
28
21
27
12
0.78%
29
22
26
11
1.55%
30
23
25
10
2.97%
31
23
24
10
2.13%
32
24
23
9
4.08%
33
25
22
8
7.46%
34
26
21
7
12.99%
35
26
20
7
10.18%
36
27
19
6
17.49%
37
28
18
5
28.25%
38
29
17
4
42.61%
39
29
16
4
36.98%
40
30
15
3
53.87%
41
31
14
2
71.89%
42
32
13
1
87.33%
43
32
12
1
84.16%
44
33
11
0
95.78%
45
34
10
0
99.00%
46
35
9
0
99.00%
47
35
8
0
99.00%
48
36
7
0
99.00%
49
37
6
0
99.00%
50
38
5
0
99.00%
51
38
4
0
99.00%
52
39
3
0
99.00%
53
40
2
0
99.00%
54
41
1
0
99.00%
55
41
0
0
99.00%
