To determine the number of free food prizes won by the next 20 patrons who spin the wheel, we will review the provided line of random numbers: "21274379713553228153".
We need to identify how many times digits representing free food (0 through 6) appear in this string. Here is the step-by-step process:
1. Identify the first digit: 2 (free food)
2. Identify the second digit: 1 (free food)
3. Identify the third digit: 2 (free food)
4. Identify the fourth digit: 7 (valet parking)
5. Identify the fifth digit: 4 (free food)
6. Identify the sixth digit: 3 (free food)
7. Identify the seventh digit: 7 (valet parking)
8. Identify the eighth digit: 9 (valet parking)
9. Identify the ninth digit: 7 (valet parking)
10. Identify the tenth digit: 1 (free food)
11. Identify the eleventh digit: 3 (free food)
12. Identify the twelfth digit: 5 (free food)
13. Identify the thirteenth digit: 5 (free food)
14. Identify the fourteenth digit: 3 (free food)
15. Identify the fifteenth digit: 2 (free food)
16. Identify the sixteenth digit: 2 (free food)
17. Identify the seventeenth digit: 8 (valet parking)
18. Identify the eighteenth digit: 1 (free food)
19. Identify the nineteenth digit: 5 (free food)
20. Identify the twentieth digit: 3 (free food)
Let's count the number of times the characters 0 through 6 appear:
- 2: appears 4 times
- 1: appears 3 times
- 4: appears 1 time
- 3: appears 3 times
- 5: appears 3 times
- 6: does not appear
Summing these values gives us:
[tex]\[ 4 + 3 + 1 + 3 + 3 = 14.\][/tex]
Checking again, we find:
[tex]\[ 2 + 1 + 2 + 4 + 3 + 1 + 3 + 5 + 5 + 3 + 2 + 2 + 1 + 5 + 3 = 15.\][/tex]
So, the best estimate of the number of free food prizes won by the next 20 patrons who spin the wheel is:
[tex]\[ \boxed{15}.\][/tex]
