4 employees drive to work in the same car. the workers claim they were late to work because of a flat tire. their managers ask the workers to identify the tire that went flat; front drivers side, front passenger side, rear driver side, or rear passenger side. If the workers didn’t really have a flat tire and each randomly selects a tire, what is the probability that all 4 workers select the same tire

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 = [tex]\frac{1}{4}[/tex]The probability that they all select front drivers side,tire is: [tex]\frac{1}{4}\times \frac{1}{4}\times \frac{1}{4}\times \frac{1}{4}=\frac{1}{256}[/tex]Similarly,The probability that they all select front passenger side, tire is: [tex]\frac{1}{256}[/tex]The probability that they all select rear driver side,tire is: [tex]\frac{1}{256}[/tex]The probability that they all select rear passenger side, tire is: [tex]\frac{1}{256}[/tex]Hence, the probability that all four workers select the same​ tire = [tex]\frac{1}{256}+ \frac{1}{256}+\frac{1}{256}+\frac{1}{256}[/tex] the probability that all four workers select the same​ tire = [tex]\frac{4}{256}=\frac{1}{64}=0.015625[/tex]Hence, the required probability is 0.015625.