22. Fix It Fast is an auto repair shop that employs 10 mechanics. Each day, the shop owner randomly picks 1 mechanic to receive a free lunch. What is the probability the shop owner will pick the same mechanic to receive a free lunch 2 days in a row?
Answer: B
The probability the shop owner will pick the same mechanic to receive a free lunch 2 days in a row is 1/100.
The scenario involves selecting one mechanic from a total of 10 mechanics each day. To find the probability of the same mechanic being chosen two consecutive days, we consider that the chance of selecting any specific mechanic on the second day, given that one was already chosen on the first day, remains 1 in 10.
A) 120
This option is incorrect as it suggests a numerical outcome that does not relate to the probability of selecting a mechanic. The probability of an event cannot exceed 1, and therefore, 120 is an invalid probability outcome.
B) 1/100
This option is correct. The chance of selecting the same mechanic on the second day after choosing one on the first day is calculated as the probability of selecting the initial mechanic (1/10) multiplied by the probability of selecting the same one again (1/10). Thus, 1/10 * 1/10 = 1/100.
C) 15
This option is incorrect because it presents a whole number that does not represent a probability. Probabilities are expressed as fractions or percentages between 0 and 1, and 15 does not fit this criterion.
D) 110
This option is also incorrect as it presents a figure that exceeds the maximum probability of 1. A probability cannot be greater than 1, making 110 a nonsensical choice in this context.
Conclusion
The correct answer, 1/100, accurately reflects the probability of selecting the same mechanic two days in a row from a pool of 10 mechanics. All other options fail to provide a valid probability and either misinterpret the question's requirements or present impossible numerical outcomes.