Answer:
The required probability is 0.015625.
Step-by-step explanation:
Consider the provided information.
There number of tires are 4.
The number of workers are 4.
The probability that individual select front drivers side tire = ![\frac{1}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D)
The probability that they all select front drivers side,tire is: ![\frac{1}{4}\times \frac{1}{4}\times \frac{1}{4}\times \frac{1}{4}=\frac{1}{256}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%5Ctimes%20%5Cfrac%7B1%7D%7B4%7D%5Ctimes%20%5Cfrac%7B1%7D%7B4%7D%5Ctimes%20%5Cfrac%7B1%7D%7B4%7D%3D%5Cfrac%7B1%7D%7B256%7D)
Similarly,
The probability that they all select front passenger side, tire is: ![\frac{1}{256}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B256%7D)
The probability that they all select rear driver side,tire is: ![\frac{1}{256}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B256%7D)
The probability that they all select rear passenger side, tire is: ![\frac{1}{256}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B256%7D)
Hence, the probability that all four workers select the same tire = ![\frac{1}{256}+ \frac{1}{256}+\frac{1}{256}+\frac{1}{256}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B256%7D%2B%20%5Cfrac%7B1%7D%7B256%7D%2B%5Cfrac%7B1%7D%7B256%7D%2B%5Cfrac%7B1%7D%7B256%7D)
the probability that all four workers select the same tire = ![\frac{4}{256}=\frac{1}{64}=0.015625](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B256%7D%3D%5Cfrac%7B1%7D%7B64%7D%3D0.015625)
Hence, the required probability is 0.015625.