Question

A state auto-inspection station has two inspection teams. team 1 is lenient and passes all automobiles of a recent vintage; team 2 rejects all autos on a first inspection because their “headlights are not properly adjusted.” four unsuspecting drivers take their autos to the station for inspection on four different days and randomly select one of the two teams. a if all four cars are new and in excellent condition, what is the probability that three of the four will be rejected? b what is the probability that all four will pass?

Answer 1

The probability of passing and rejection is equally likely given that one of the teams are randomly selected for the inspection and that the drivers are unsuspecting.

Thus, P(passing) = 1/2
P(rejection) = 1/2

Part A:

The probability that three of the four will be rejected is given by


`P(RRRP)=\ ^4C_3*\left( (1)/(2) \right)^3*\left( (1)/(2) \right) \\ \\ =4* (1)/(8)* (1)/(2) =(1)/(4)=25\%`



Part B:

The probability that all four will pass is given by


`P(PPPP)=\ ^4C_4*\left( (1)/(2) \right)^4\\ \\ =1* (1)/(16) =(1)/(16)=6.25\%`