7 A Lost Property office is open 7 days a week. It may be assumed that items are handed in to the office randomly, singly and independently.
- State another condition for the number of items handed in to have a Poisson distribution.
It is now given that the number of items handed in per week has the distribution \(\operatorname { Po } ( 4.0 )\).
- Find the probability that exactly 2 items are handed in on a particular day.
- Find the probability that at least 4 items are handed in during a 10-day period.
- Find the probability that, during a certain week, 5 items are handed in altogether, but no items are handed in on the first day of the week.