Question

suppose vehicles arrive at COVID-19 drive-through test station with the rate of 24 per hour on average. Round the values to the nearest hundredth if needed.
1/ What is the probability that exactly one vehicle arrives during next five minutes?
2/ What is the probability that there will be at least one vehicle during the next five minutes?
3/ Suppose that an arriving vehicle will have test positive with probability .01. What is the probability that at least 1 vehicle arrives during the next 5 minutes and has test positive?

Answer 1

1) expected number of vehicle in next 5 minute =1*24/(60*24) =1/12

probability that exactly one vehicle arrives during next five minutes =P(X=1)=e^-1/12*(1/12)¹/1!=0.0767

2)probability that there will be at least one vehicle during the next five minutes =P(X>=1)

=1-P(X=0)=1-e^-1/12 =0.0800

3)

expected test postiive vehicle =(1/12)*0.01 =1/1200

=P(at least one arrive and  has test positive) =P(X>=1) =1-P(X=0)=1-e^-1/1200 =0.000833