Bob’s ties
Problem: Bob has 7 different ties. He works a five day week in the office of the Inland Revenue.
Design and carry out a simulation to calculate the probability that Bob wears the same tie more than
once in a five day week. You may assume that he chooses a tie randomly each morning.
Problem:
What is the probability that Bob wears the same tie more than once in a five day week?
Tools:
I will use the randbetween tool in excel to do my simulation.
The formula I will use is =randbetween (1, 7). I am using (1, 7) because the numbers 1, 2, 3, 4, 5, 6,
7 will represent the seven ties that Bob can choose to wear on any of the 5 days.
Trials:
I will be doing 30 trials.
Each trial will consist of generating a random number between 1 and 7 five times. A random number
created 5 times will represent the five days – Monday through to Friday that he wears a tie.
A successful trial will be when a tie is repeated at least once.
Results:
Trial #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
D1
6
4
4
3
7
2
5
1
2
1
6
2
4
7
7
3
5
1
4
7
3
3
3
2
7
4
D2
1
7
1
7
3
6
5
2
1
4
5
4
4
2
4
3
3
7
5
4
1
6
6
1
2
6
D3
4
4
4
2
3
6
3
6
5
1
3
7
1
7
4
7
1
3
2
1
2
1
5
5
4
2
D4
1
2
5
2
6
3
4
3
1
2
2
7
1
6
3
6
4
2
5
1
6
1
7
5
1
2
D5
2
6
1
3
7
1
7
5
2
4
4
6
4
1
4
4
1
7
1
4
3
5
1
5
6
7
Any tie repeated at least
twice?
y
y
y
y
y
y
y
n
y
y
n
y
y
y
y
y
y
y
y
y
y
y
n
y
n
y
27
28
29
30
1
4
2
5
4
1
4
5
3
2
4
7
3
6
6
6
Probability of a repeat:
5
7
4
3
y
y
y
y
0.866666667
Calculation:
Probability (Y) = 26/30 = 0.87 OR 87%
Answer:
What is the probability that Bob wears the same tie more than once in a five day week?
Probability that Bob wears the same tie more than once in a 5 day week is 0.87 (87%).