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If 30 tickets are numbered consecutively from 1 to 30, and 2 tickets aré selected at random without replacement, find expected (sum of the numbers on the two tickets) and find the variance (sum of the numbers on the two tickets).

Question

If 30 tickets are numbered consecutively from 1 to 30, and 2 tickets aré selected at random without replacement, find expected (sum of the numbers on the two tickets) and find the variance (sum of the numbers on the two tickets).

check_circleAnswer
Step 1

let X be the sum of numbers. X can range from 3 to 59.

Make the 30 by 30 grid for ease of calculations where at the intersection of any two numbers lies their sum. 

It is impossible to fit the entire worksheet here but i've written formulae and displayed Excel functions so that you can do this easily. I have also included answer screen so that you can verify your answers.

AO AD
K
Y
A0
R
x
C
D
M
N
F
T
z
AD
AZ
AH
20
21
20 21 22 230
22
21
4
6
10
1
7 9 10 1 4 15 162
7
14
151
16
17
19
23
24
24
25 26
27
28
29
30
31
1
5
17
27
20
29 J
30
8
12 b 16 1 20 21 22 2 24 25 26 27 2 29 30 31 32
3
0
5
7
23
2
3
8 11 12 13 5 18 19 20 21 22 23 24 2 26 2 28 29 30 1 32 33
6 7 0 1 1 12 13 14 7 18 19 2 21 22 23 2 25 26 27 28 29 3 31 32 33 3
6 0
h
6
5 7 8 13 14 5 17 8 1 20 21 22 23 24 25 2 27 28 29 30 31 32 33 34 35
7 2 13 5 1 1 1 20 21 22 23 2 25 26 27 28 29 30 31 32 33 34 35 3
7 8 10 3 12 13 16 1 20 21 22 23 24 25 2s 27 28 2 30 3 32 33 34 35 36 37
8 13 14 0 17 18 9 20 21 22 23 24 25 26 27 28 2 3 31 32 33 34 36 37 38
6
IC
20 2 22 23 24 2 2a 32 3 3 6 37 38 39
10 11 13 6 15 17 2 19 0 2 22 23 24 25 2 27 28 29 30 31 32 33 34 35 37 39 40
13
2
5
14
26
27
29
30
31
35
11
1 12 14 7 16 17 3 20 21 0 2 24 25 26 27 28 29 30 31 4 35 36 37 3 39 40 41
12 3 15 12 1 21 22 23 25 26 2 2 30 31 32 3 24 5 3 3 2 40 41 42
s 13 16 18 9 20 5 22 23 21 0 27 29 2 30 31 32 33 34 3 3 38 3 40 1 42 3
1 17 10 9 20 2 23 2 2 2 27 0 29 3 3 32 33 34 3 3 3 38 39 0 42 43 44
1 1 20 2122 724 25 2 28 29 0 31 33 3 3 04 4243 5
2 28 2 4 29 30 1 33 34 35 3 3 3 39 40 41 42 43 44 45 46
TO
0
37
40
46
1 20 13 22 23 24 26 2 2 30 3132 5 36 37 3 40 4 42 43 4445 46 47
20 18 20 21 4 23 24 0 27 28 29 6 3 02 33 35 07 38 3 40 42 43 44 45 46 47 48
21 1 20 2122 15 24 2 26 28 29 7 32 3334 3 7 0 39 4 41 42 43 4 546 47 48 4
22 2 21 22 2 27 2 23 30 1 33 4 3 4 3 3 43 44 45 6 7 4 4 50 5t
39 0 41 42 43 44 45 4 47 4 49 50
20
23
25
23 21 22 23 24 17 2 2 2 31 3 3 3 4 2 43 45 4 47 8 4 e 5 52
30
32
48
48
49
24 22 23 24 25 1 27 2 2 1 32 9 4 35 3 5 3 3 0
18
28
33
30
35
36
39
41
0
46
51
4
23 24 25 26 13 28 29 30 15 32 33 34 11 3 37 39 7 40 1 42 3 45 47 48 49 50 51 52
24 2 2 27 20 29 30 3 16 32 34 3 38 39 4 42 4 4 45 46 47 49 50 61 62 63
52
25
54
2 25 2 27 28 21 3D 31 3 7 34 35 13 38 39 40 42 43 4 5 47 48 0 1 4 55
5
26
28 27 28 29 22 31 32 33 3 37 3 0 41 2 43 4 s 47 48 49 2 53 65
27 28 2 30 23 32 33 34 36 3 40 4 42 4 45 6 48 4 50 3 52 53 0
28 23 30 31 24 33 34 35 20 37 38 33 4 42 43 12 45s 46 7 4
29
28
25
5
53 54
7
30
17 42 4 44
44 4
39
9
59
25
26
30
31
2
32
34
35
36
37
21
38
40
49
3
46
47
48
50
51
52
5
54
56
1
30
31
33
35
38:
22
39
40
40
14
47
48
49
10
51
6
55
5
57
323
55
34
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AO AD K Y A0 R x C D M N F T z AD AZ AH 20 21 20 21 22 230 22 21 4 6 10 1 7 9 10 1 4 15 162 7 14 151 16 17 19 23 24 24 25 26 27 28 29 30 31 1 5 17 27 20 29 J 30 8 12 b 16 1 20 21 22 2 24 25 26 27 2 29 30 31 32 3 0 5 7 23 2 3 8 11 12 13 5 18 19 20 21 22 23 24 2 26 2 28 29 30 1 32 33 6 7 0 1 1 12 13 14 7 18 19 2 21 22 23 2 25 26 27 28 29 3 31 32 33 3 6 0 h 6 5 7 8 13 14 5 17 8 1 20 21 22 23 24 25 2 27 28 29 30 31 32 33 34 35 7 2 13 5 1 1 1 20 21 22 23 2 25 26 27 28 29 30 31 32 33 34 35 3 7 8 10 3 12 13 16 1 20 21 22 23 24 25 2s 27 28 2 30 3 32 33 34 35 36 37 8 13 14 0 17 18 9 20 21 22 23 24 25 26 27 28 2 3 31 32 33 34 36 37 38 6 IC 20 2 22 23 24 2 2a 32 3 3 6 37 38 39 10 11 13 6 15 17 2 19 0 2 22 23 24 25 2 27 28 29 30 31 32 33 34 35 37 39 40 13 2 5 14 26 27 29 30 31 35 11 1 12 14 7 16 17 3 20 21 0 2 24 25 26 27 28 29 30 31 4 35 36 37 3 39 40 41 12 3 15 12 1 21 22 23 25 26 2 2 30 31 32 3 24 5 3 3 2 40 41 42 s 13 16 18 9 20 5 22 23 21 0 27 29 2 30 31 32 33 34 3 3 38 3 40 1 42 3 1 17 10 9 20 2 23 2 2 2 27 0 29 3 3 32 33 34 3 3 3 38 39 0 42 43 44 1 1 20 2122 724 25 2 28 29 0 31 33 3 3 04 4243 5 2 28 2 4 29 30 1 33 34 35 3 3 3 39 40 41 42 43 44 45 46 TO 0 37 40 46 1 20 13 22 23 24 26 2 2 30 3132 5 36 37 3 40 4 42 43 4445 46 47 20 18 20 21 4 23 24 0 27 28 29 6 3 02 33 35 07 38 3 40 42 43 44 45 46 47 48 21 1 20 2122 15 24 2 26 28 29 7 32 3334 3 7 0 39 4 41 42 43 4 546 47 48 4 22 2 21 22 2 27 2 23 30 1 33 4 3 4 3 3 43 44 45 6 7 4 4 50 5t 39 0 41 42 43 44 45 4 47 4 49 50 20 23 25 23 21 22 23 24 17 2 2 2 31 3 3 3 4 2 43 45 4 47 8 4 e 5 52 30 32 48 48 49 24 22 23 24 25 1 27 2 2 1 32 9 4 35 3 5 3 3 0 18 28 33 30 35 36 39 41 0 46 51 4 23 24 25 26 13 28 29 30 15 32 33 34 11 3 37 39 7 40 1 42 3 45 47 48 49 50 51 52 24 2 2 27 20 29 30 3 16 32 34 3 38 39 4 42 4 4 45 46 47 49 50 61 62 63 52 25 54 2 25 2 27 28 21 3D 31 3 7 34 35 13 38 39 40 42 43 4 5 47 48 0 1 4 55 5 26 28 27 28 29 22 31 32 33 3 37 3 0 41 2 43 4 s 47 48 49 2 53 65 27 28 2 30 23 32 33 34 36 3 40 4 42 4 45 6 48 4 50 3 52 53 0 28 23 30 31 24 33 34 35 20 37 38 33 4 42 43 12 45s 46 7 4 29 28 25 5 53 54 7 30 17 42 4 44 44 4 39 9 59 25 26 30 31 2 32 34 35 36 37 21 38 40 49 3 46 47 48 50 51 52 5 54 56 1 30 31 33 35 38: 22 39 40 40 14 47 48 49 10 51 6 55 5 57 323 55 34

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Step 2

Don't be intimidated by the table. After you fill in the first 2 lines, just drag. Make sure you use the dollar signs wherever required. Notice how 1,1 or 2,2 or 3,3 are all zero. That is because we are drawing without replacement so any two tickets that are drawn will be different from each other..

E
G
H
A
5
2
1
3
f6
7
10
-sa53 - F2
SB53- 12
- 5853+ E2
- 5853- G2
- 5853+ H2
SB53-12
SBS3-D2
-SB53+ K2
-S8S3+L2
-es4 C2
-SBS5+ C2
-SB56+ C2
-5854 L2
5855-12
- 5856 + L2
2
-5854 E2
-se54 F2
-$854 G2
-$B54. H2
-SBS4+12
-SB54+12
-SB54+K2
0
SB55+12
-$B56 + 12
SBS5 02
5855-G2
-$B56 + G2
SBss-H2
-SB$ 5 - H2
-5853 H6
-SB55+ K2
0
5855-F2
SBS5+12
-SB56 E2
-SB56- 12
SB56 K2
6
SB56+02
-5853 F6
5
-SB53 C6
854 C6
-SB55 C6
-SB56 C6
-SB53+D6
-SB53 E6
0
-SBS3 16
=$a54 + 16
SBS3 J6
-SB53+K6
-5853 L6
- s854+L6
-S8$5 + L6
-s856 L6
-SB54+ G6
-SBS4 + 16
-5854+F6
6
-SB54+06
SB54+E6
-SB54+K6
-SB55+ E6
-5855+ F6
-$855+ G6
- SBS5 H6
-SB55+ J6
-SB55+ K5
7
SBS5 D6
-SB56 K6
-5856+F6
- 585 3 - F10
-5B56+16
10
8
-S856+06
-s856 E6
-5856 G6
-SB56+ H6
- SB53+ E10
-SB54 E10
-Se55 E10
- SB56 - E 10
-5B53 E14
- 5B$ 3 - G10
- $a53- H10
-SBS3+C10
=SBS3+110
-sas3 - L10
11
SBS3+D10
SBS3+ 1 10
S8s4+F10
5855 F10
- S856 - F10
- SBS4+ 1 10
B54+ C10
-SB54+D10
-$854+ G10
-SB54+ H10
SBS4+J10
-SB54+ K10
12
10
-SB55 C10
-SB56 C10
13
11
-sess+010
-5855 G10
-5855+H10
-SB55+110
-SBS5 130
-SBS5 K10
-5855 L10
- 5856 -G10
-S853 G14.
-SB54 G14
-$B56 - H10
-SB56- 1 10
-S856 - L10
-5B55- 1 10
14
12
SB56-010
=SB56 K10
-SBS3 J24
-SBS4 - 114
SB53+014
SB53+114
SB53+C14
-$853+ F14
-SB53 H14
-SBS3+K14
Ses3 L14
15
13
-5e54+K14
-5855-K14
-854 C14
-5854 F14
-$854-H14
16
14
-SB54+014
-SB54+E14
-SBS4+114
-S854+L14
- SB55 - 1 14
-SB56 114
-$855- H14
-$856 H14
- SB53- H 18
-5B55-C14
- S855 - G14
$B55+114
17
15
-SB55-014
-5855+E14
-5855 - F14
-5855 - L14
SB56 C14
-SB56 J14
-SBS3- 138
-5B54 - J18
-SB55 118
-S856 L14
18
-SB56 014
-SB56 E14
-se56 F14
-s856 G14
-SB56+ K14
16
- SB53+E18
-SB$4+E18
-5853- L18
19
17
-SBS3+C18
-SB53+018
-S8S3+F18
-5853-G18
-SBS3+118
$853+K18
18
8$4+C18
-SB54+D18
-5854+F18
-5854 + G18
-5855 G18
-s856- G18
-5BS4. H18
-$B54+ 1 18
SB54+K18
-5854+L18
20
-SB55 C18
-5855 F18
-S855 E18
SBS6+ E18
-5B55 K18
21
19
-SB55 018
-5855 H18
-SBS5 1 18
-s855 L18
-SB56- 118
SBS6+C18
SB56+018
SB56+F18
|-SB56-H18
SB56+K18
-SB56-118
22
20
-5856 118
-SB53 + 122
-SBS3- C22
-854 C22
-SB55- C22
-SB56+ C22
-5853 F22
-SBS3+D22
-SBS3 E22
S854 E22
-s855- E22
-SB53+G22
SBS3+ H22
-5854+H22
-SB55+ H22
-$855 H22
-Se53 H26
- SB54 - H26
5B53+ 122
-SB53+ K22
-S853+ L22
23
21
-S854 G22
-5854+F22
24
22
-sB54 022
SB54+122
-SB55+ 122
#$B55 + 122
SB54+122
-5854+K22
-S854 L22
-5855-G22
25
23
-$B55 +D22
=S855+ F22
- S B55- 122
-SB55+ K22
-S855 + L22
-SB56+ D22
-$856+ F22
-5856 G22
-5853 G26
SBS6-122
-SBS3 126
-$BS4 + 126
-S856 L22
26
24
-S856 E22
-SB56+ K22
5853+F26
- 5854+ F26
-s853 E26-
-$B54- E26
-ses3+126
-s853 L26
27
25
-se53 C26
a54-C26
-SB55 + C26
5BS C26
-$ BS3- C30
854 C30
-SBS3+026
s853+K26
=SB$4-G26,
$B$4-126
SB54+ K26
- 5854 L26
28
26
SBS4-025
S855 H26
-ses6 + H26
-SB55+026
-5855+ E26
-s8s5+F26
-S85+ G26
-SBS5+126
B55+J25
-SB56 126
SB53-130
-SBS5+K26
-5855+ L26
29
27
-5856 G26
28
-SB56 026
SBS6+126
30
-ses6 E26
-5856+F26
s856+K26
-5856+126
- SB53 + E30
-SB54 E30
-SB53- H301
-SB53- 130
- S853- L30
31
291
-SB53-D30
-SB53+ F30
=5853-G30
-5853+ K30
$854 L30
-$854 H30
32
30
-5B54+030
-S854 G30
SBS4 130
SBS4 130
-S854+ K30
S854 F30
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Image Transcriptionclose

E G H A 5 2 1 3 f6 7 10 -sa53 - F2 SB53- 12 - 5853+ E2 - 5853- G2 - 5853+ H2 SB53-12 SBS3-D2 -SB53+ K2 -S8S3+L2 -es4 C2 -SBS5+ C2 -SB56+ C2 -5854 L2 5855-12 - 5856 + L2 2 -5854 E2 -se54 F2 -$854 G2 -$B54. H2 -SBS4+12 -SB54+12 -SB54+K2 0 SB55+12 -$B56 + 12 SBS5 02 5855-G2 -$B56 + G2 SBss-H2 -SB$ 5 - H2 -5853 H6 -SB55+ K2 0 5855-F2 SBS5+12 -SB56 E2 -SB56- 12 SB56 K2 6 SB56+02 -5853 F6 5 -SB53 C6 854 C6 -SB55 C6 -SB56 C6 -SB53+D6 -SB53 E6 0 -SBS3 16 =$a54 + 16 SBS3 J6 -SB53+K6 -5853 L6 - s854+L6 -S8$5 + L6 -s856 L6 -SB54+ G6 -SBS4 + 16 -5854+F6 6 -SB54+06 SB54+E6 -SB54+K6 -SB55+ E6 -5855+ F6 -$855+ G6 - SBS5 H6 -SB55+ J6 -SB55+ K5 7 SBS5 D6 -SB56 K6 -5856+F6 - 585 3 - F10 -5B56+16 10 8 -S856+06 -s856 E6 -5856 G6 -SB56+ H6 - SB53+ E10 -SB54 E10 -Se55 E10 - SB56 - E 10 -5B53 E14 - 5B$ 3 - G10 - $a53- H10 -SBS3+C10 =SBS3+110 -sas3 - L10 11 SBS3+D10 SBS3+ 1 10 S8s4+F10 5855 F10 - S856 - F10 - SBS4+ 1 10 B54+ C10 -SB54+D10 -$854+ G10 -SB54+ H10 SBS4+J10 -SB54+ K10 12 10 -SB55 C10 -SB56 C10 13 11 -sess+010 -5855 G10 -5855+H10 -SB55+110 -SBS5 130 -SBS5 K10 -5855 L10 - 5856 -G10 -S853 G14. -SB54 G14 -$B56 - H10 -SB56- 1 10 -S856 - L10 -5B55- 1 10 14 12 SB56-010 =SB56 K10 -SBS3 J24 -SBS4 - 114 SB53+014 SB53+114 SB53+C14 -$853+ F14 -SB53 H14 -SBS3+K14 Ses3 L14 15 13 -5e54+K14 -5855-K14 -854 C14 -5854 F14 -$854-H14 16 14 -SB54+014 -SB54+E14 -SBS4+114 -S854+L14 - SB55 - 1 14 -SB56 114 -$855- H14 -$856 H14 - SB53- H 18 -5B55-C14 - S855 - G14 $B55+114 17 15 -SB55-014 -5855+E14 -5855 - F14 -5855 - L14 SB56 C14 -SB56 J14 -SBS3- 138 -5B54 - J18 -SB55 118 -S856 L14 18 -SB56 014 -SB56 E14 -se56 F14 -s856 G14 -SB56+ K14 16 - SB53+E18 -SB$4+E18 -5853- L18 19 17 -SBS3+C18 -SB53+018 -S8S3+F18 -5853-G18 -SBS3+118 $853+K18 18 8$4+C18 -SB54+D18 -5854+F18 -5854 + G18 -5855 G18 -s856- G18 -5BS4. H18 -$B54+ 1 18 SB54+K18 -5854+L18 20 -SB55 C18 -5855 F18 -S855 E18 SBS6+ E18 -5B55 K18 21 19 -SB55 018 -5855 H18 -SBS5 1 18 -s855 L18 -SB56- 118 SBS6+C18 SB56+018 SB56+F18 |-SB56-H18 SB56+K18 -SB56-118 22 20 -5856 118 -SB53 + 122 -SBS3- C22 -854 C22 -SB55- C22 -SB56+ C22 -5853 F22 -SBS3+D22 -SBS3 E22 S854 E22 -s855- E22 -SB53+G22 SBS3+ H22 -5854+H22 -SB55+ H22 -$855 H22 -Se53 H26 - SB54 - H26 5B53+ 122 -SB53+ K22 -S853+ L22 23 21 -S854 G22 -5854+F22 24 22 -sB54 022 SB54+122 -SB55+ 122 #$B55 + 122 SB54+122 -5854+K22 -S854 L22 -5855-G22 25 23 -$B55 +D22 =S855+ F22 - S B55- 122 -SB55+ K22 -S855 + L22 -SB56+ D22 -$856+ F22 -5856 G22 -5853 G26 SBS6-122 -SBS3 126 -$BS4 + 126 -S856 L22 26 24 -S856 E22 -SB56+ K22 5853+F26 - 5854+ F26 -s853 E26- -$B54- E26 -ses3+126 -s853 L26 27 25 -se53 C26 a54-C26 -SB55 + C26 5BS C26 -$ BS3- C30 854 C30 -SBS3+026 s853+K26 =SB$4-G26, $B$4-126 SB54+ K26 - 5854 L26 28 26 SBS4-025 S855 H26 -ses6 + H26 -SB55+026 -5855+ E26 -s8s5+F26 -S85+ G26 -SBS5+126 B55+J25 -SB56 126 SB53-130 -SBS5+K26 -5855+ L26 29 27 -5856 G26 28 -SB56 026 SBS6+126 30 -ses6 E26 -5856+F26 s856+K26 -5856+126 - SB53 + E30 -SB54 E30 -SB53- H301 -SB53- 130 - S853- L30 31 291 -SB53-D30 -SB53+ F30 =5853-G30 -5853+ K30 $854 L30 -$854 H30 32 30 -5B54+030 -S854 G30 SBS4 130 SBS4 130 -S854+ K30 S854 F30

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Step 3

Now we know that sum can range from 3 to 59 , let's count how many occurences of each sum are which in turn will help us calculate ...

AF
AG
AJ
AH
Al
AG
AH
Al
29
30 Sum
Chances
Probability
Probability
COUNTIF(C$3:AF$32,AG3)AH3/(29*30)
COUNTIF(C$3:AF$32,AG4) AH4/(29*30)
COUNTIF(C$3:AF$32,AG5) AH5/(29*30)
COUNTIF(C$3:AF$32,AG6) AH6/ (29*30)
COUNTIF(C$3:AF$32,AG7) AH7/(29*30)
COUNTIF(C$3:AF$32,AG8) AH8/(29*30)
COUNTIF(C$3:AF$32,AG9) AH9/(2
COUNTIF(C$3:AF$32,AG10) AH10/(29*30)
COUNTIF(C$3:AF$32,AG11) -AH11/(29 30)
COUNTIF(C$3:AF$32,AG12) AH12/(29*30)
COUNTIF(C$3:AF$32,AG13) -AH13/(29*30)
=COUNTIF(C$3:AF$32,AG14) =AH14/ (29*30)
COUNTIF(C$3:AF$32,AG15) -AH15/(29*30)
COUNTIF(C$3:AF$32,AG16 ) -AH16/(29*30)
COUNTIF(C$3:AF$32,AG17) AH17/(29*30)
COUNTIF(C$3:AF$32,AG18) -AH18/(29*30)
COUNTIF(C$3:AF$32,AG19) -AH19/(29*30)
COUNTIF(C$3:AF$32,AG20) AH20/(29*30)
COUNTIF(C$3:AF$32,AG21) -AH21/(29*30)
COUNTIF(C$3:AF$32,AG22) =AH22/(29*30)
COUNTIF(C$3:AF$32,AG23) -AH23/(29*30)
COUNTIF(C$3:AF$32,AG24) =AH24/ (29*30)
COUNTIF(C$3:AF$32,AG25) AH25 / (29*30)
COUNTIF(C$3:AF$32,AG26) AH26/(29*30)
COUNTIF(C$3:AF$32,AG27) -AH27/ (29*30)
-COUNTIF(C$3:AF$32,AG28) AH28/(29*30)
COUNTIF(C$3:AF$32,AG29) -AH29/(29*30)
Chances
Sum
30
31
3
8 0.009195
3
31
32
8 0.009195
4
10 0.011494
32
33
5
5
10 0.011494
33
34
6
6
34
35
7
11 0.012644
7
35
36
8
11 0.012644
8
36
37
9
12 0.013793
9
37
38
10
12 0.013793
10
38
39
11
13 0.014943
11
39
40
12
13 0.014943
12
40
41
13
15 0.017241
13
41
42
14
15 0.017241
14
42
43
15
16 0.018391
15
43
44
16
16 0.018391
16
44
45
17
17
0.01954
17
45
46
18
17
0.01954
18
46
47
19
18
0.02069
19
47
48
20
0.02069
18
20
48
21
20 0.022989
49
21
49
50
22
20 0.022989
22
50
51
23
21 0.024138
23
51
52
24
21 0.024138
24
52
53
25
22 0.025287
25
54
22 0.025287
53
26
26
23 0.026437
54
55
27
27
56
28
55
23 0.026437
28
57
29
25 0.028736
56
29
N
co
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AF AG AJ AH Al AG AH Al 29 30 Sum Chances Probability Probability COUNTIF(C$3:AF$32,AG3)AH3/(29*30) COUNTIF(C$3:AF$32,AG4) AH4/(29*30) COUNTIF(C$3:AF$32,AG5) AH5/(29*30) COUNTIF(C$3:AF$32,AG6) AH6/ (29*30) COUNTIF(C$3:AF$32,AG7) AH7/(29*30) COUNTIF(C$3:AF$32,AG8) AH8/(29*30) COUNTIF(C$3:AF$32,AG9) AH9/(2 COUNTIF(C$3:AF$32,AG10) AH10/(29*30) COUNTIF(C$3:AF$32,AG11) -AH11/(29 30) COUNTIF(C$3:AF$32,AG12) AH12/(29*30) COUNTIF(C$3:AF$32,AG13) -AH13/(29*30) =COUNTIF(C$3:AF$32,AG14) =AH14/ (29*30) COUNTIF(C$3:AF$32,AG15) -AH15/(29*30) COUNTIF(C$3:AF$32,AG16 ) -AH16/(29*30) COUNTIF(C$3:AF$32,AG17) AH17/(29*30) COUNTIF(C$3:AF$32,AG18) -AH18/(29*30) COUNTIF(C$3:AF$32,AG19) -AH19/(29*30) COUNTIF(C$3:AF$32,AG20) AH20/(29*30) COUNTIF(C$3:AF$32,AG21) -AH21/(29*30) COUNTIF(C$3:AF$32,AG22) =AH22/(29*30) COUNTIF(C$3:AF$32,AG23) -AH23/(29*30) COUNTIF(C$3:AF$32,AG24) =AH24/ (29*30) COUNTIF(C$3:AF$32,AG25) AH25 / (29*30) COUNTIF(C$3:AF$32,AG26) AH26/(29*30) COUNTIF(C$3:AF$32,AG27) -AH27/ (29*30) -COUNTIF(C$3:AF$32,AG28) AH28/(29*30) COUNTIF(C$3:AF$32,AG29) -AH29/(29*30) Chances Sum 30 31 3 8 0.009195 3 31 32 8 0.009195 4 10 0.011494 32 33 5 5 10 0.011494 33 34 6 6 34 35 7 11 0.012644 7 35 36 8 11 0.012644 8 36 37 9 12 0.013793 9 37 38 10 12 0.013793 10 38 39 11 13 0.014943 11 39 40 12 13 0.014943 12 40 41 13 15 0.017241 13 41 42 14 15 0.017241 14 42 43 15 16 0.018391 15 43 44 16 16 0.018391 16 44 45 17 17 0.01954 17 45 46 18 17 0.01954 18 46 47 19 18 0.02069 19 47 48 20 0.02069 18 20 48 21 20 0.022989 49 21 49 50 22 20 0.022989 22 50 51 23 21 0.024138 23 51 52 24 21 0.024138 24 52 53 25 22 0.025287 25 54 22 0.025287 53 26 26 23 0.026437 54 55 27 27 56 28 55 23 0.026437 28 57 29 25 0.028736 56 29 N co

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