Question

(4) You can reach your office from home either directly via I-77 or by first taking I-271 north and then taking SR-8 south. There’s no other way of reaching your office. On a usual weekday morning, the chances of I-77 being closed due to an accident is 0.1, that of I-271 north being closed due to an accident is 0.08 and that of SR-8 south being closed is 0.05. Assuming that the traffic conditions on these 3 highways are independent of one another, what are your chances of reaching the office on a typical weekday morning? Suppose the traffic condition on any particular day is independent of that on any other day. What are the chances that, in the next 3 days, you will fail to reach your office twice due to accident-related traffic congestion?

Answer 1

(a)

P( reaching the office on a typical weekday morning ) = 1 - P( not reaching the office on a typical weekday morning )

= 1 - (0.1 X 0.08 X 0.05)

= 1 - 0.0004

= 0.9996

So,

Answer is:

0.9996

(b)

Binomial Distribution

n =3

p = 0.0004

So,

q = 1 - p = 0.9996

So,

Answer is:

0.0000004798