Although illegal, overloading is common in the trucking industry. Minnesota Department of Transportation (MDOT) engineers monitored the movements of overweight trucks on an interstate highway using an unmanned, computerized scale that is built into the highway. Unknown to the truckers, the scale weighed their vehicles as they passed over it. One week, over 400 five-axle trucks were deemed to be overweight. The table at the bottom of the page shows the proportion of these overweight trucks that were detected each day of the week. Assume the daily distribution of overweight trucks remains the same from week to week.

a. If 200 overweight trucks are detected during a singl week, what is the probability that 50 are detected on Monday, 50 on Tuesday, 30 on Wednesday, 30 on Thursday, 20 on Friday, 10 on Saturday, and 10 on Sunday?
b. If 200 overweight trucks are detected during a single week, what is the probability that at least 50 are detected on Monday?