To get to work, a commuter must cross train tracks. the time the train arrives varies slightly from day to day, but the commuter estimates that he'll get stopped on about 15% of work days. during a certain 5-day work week, what is the probability that he doesn't get stopped all week long?

To solve this, we use the binomial probability equation:

P = [n! / (n - r) ! r!] * p^r * q^ (n - r)

where n is the total number of days = 5, r is number of days he get stopped = 0, p is probability he gets stopped = 0.15, q is 1 - p = 0.85

P = [5! / (5 - 0) ! 0!] * 0.15^0 * 0.85^ (5 - 0)

P = 0.4437

Hence about 44.37% he does not get stop at all.