To solve this question, follow these steps:
1. Understand the Problem:
- We are asked to determine the probability that at least four boys need to be selected before finding one who commutes to school by bicycle.
- Numbers 0 to 3 represent boys who commute by bicycle, while numbers 4 to 9 represent boys who do not commute by bicycle.
2. Extract and Flatten the Digits from the Table:
The provided table of randomly generated numbers is:
```
003, 448, 311, 790, 832
265, 843, 608, 354, 736
578, 994, 968, 895, 754
660, 340, 085, 622, 968
346, 353, 312, 544, 167
978, 005, 371, 146, 607
323, 337, 821, 617, 892
976, 985, 448, 830, 409
549, 804, 464, 50, 5
147, 317, 789, 915, 267
```
Consider each digit individually. Combine all digits into a single sequence:
```
0, 0, 3, 4, 4, 8, 3, 1, 1, 7, 9, 0, 8, 3, 2, 6, 5, 8, 4, 3, 6, 0, 8, 3, 5, 4, 5, 7, 8, 9, 9, 4, 9, 6, 8, 8, 9, 5, 7, 5, 4, 6, 6, 0, 3, 4, 0, 0, 8, 5, 6, 2, 2, 9, 6, 8, 3, 4, 6, 3, 5, 3, 3, 1, 2, 5, 4, 4, 1, 6, 7, 9, 7, 8, 0, 0, 5, 3, 7, 1, 1, 4, 6, 6, 0, 7, 3, 2, 3, 3, 3, 7, 8, 2, 1, 6, 1, 7, 8, 9, 2, 9, 7, 6, 9, 8, 5, 4, 4, 8, 8, 3, 0, 4, 0, 9, 5, 4, 9, 8, 0, 4, 4, 6, 4, 5, 0, 5, 0, 1, 4, 7, 3, 1, 7, 7, 8, 9, 9, 1, 5, 2, 6, 7
```
3. Count the Digits Representing Boys Commuting by Bicycle:
Iterate through the digits and count how many represent boys commuting by bicycle (digits: 0, 1, 2, 3).
4. Find the Position of 4th Boy Commuting by Bicycle:
- Iterate through the flattened list and count occurrences of digits 0, 1, 2, 3.
- Stop after finding the 4th such digit.
Let's do this step-by-step:
```plaintext
First 4 commutes found at positions: 0, 1, 2, 6 (0-indexed, actual sequence positions: 1, 2, 3, 7)
```
Therefore, we have to select 7 boys to guarantee that we have found at least four boys commuting by bicycle.
Answer:
The probability that you must select at least four boys to find one who commutes by bicycle is 7.
