Question

Between the hours of 2am and 3am, three cars per minute pass a toll booth. This is true for all 7 days of the week

1. Find the probability that 8 or more cars pass the toll booth for the 2 minute period from 2:01 am through 2:02 am on a given Monday.

2. Find the probability that 8 or more cars pass the toll booth for the 2 minute period from 2:01 am through 2:02 am on a given Monday, AND that 8 or more cars pass the toll booth

Answer 1

1)

Cars pass per minute = 3

Cars pass per 2 minute = 3 *2 = 6

Mean/Expected number of events of interest: λ = 6

P(X=x) = e-λλx/x!

X	P(X)
0	0.0025
1	0.0149
2	0.0446
3	0.0892
4	0.1339
5	0.1606
6	0.1606
7	0.1377

P(x>=8) = 1 - [P(X=0) + P(X=1) +...........+P(X=7)]

= 1 - 0.7440

= 0.256

2)

Here question after AND seems to be missing the information. If not, then it is same as above.

Please revert back in case of any doubt.

Please upvote. Thanks in advance.