Rationale
The probability the shop owner will pick the same mechanic to receive a free lunch 2 days in a row is 1/100.
Since there are 10 mechanics, the chance of selecting the same mechanic on both days is calculated by multiplying the probability of choosing any one mechanic on the first day (1) by the probability of choosing that same mechanic again on the second day (1/10). This results in a probability of 1/10 for the first selection and 1/10 for the second selection, leading to a combined probability of (1/10) * (1/10) = 1/100.
A) 120
The number 120 does not represent a probability but rather could be mistakenly interpreted as a potential arrangement of mechanics. However, probabilities must be between 0 and 1, and 120 does not fit within this range.
B) 1/100
This choice accurately reflects the probability of selecting the same mechanic two days in a row. With 10 mechanics, the chance of selecting one specific mechanic on the first day is 1, and the chance of selecting the same mechanic again is 1/10, leading to a total probability of 1/100.
C) 15
Similar to choice A, the number 15 does not represent a valid probability. Probabilities must be expressed as fractions or decimals between 0 and 1, and 15 exceeds this range, making it an invalid choice.
D) 110
This option, like A and C, is not a valid probability value. Probabilities cannot exceed 1, and 110 is far outside the acceptable range of probability values, rendering it incorrect.
Conclusion
In summary, the probability of selecting the same mechanic for a free lunch two days in a row at Fix It Fast is correctly represented by 1/100. This is derived from understanding the basic principles of probability, where the likelihood of repeated events is determined by multiplying the probabilities of each individual event. The other options presented do not conform to the definition of probability, reinforcing the importance of calculating probabilities within the appropriate range.
