5. A school photocopier breaks down randomly at a rate of 15 times per year.
- Find the probability that there will be exactly 3 breakdowns in the next month.
- Show that the probability that there will be at least 2 breakdowns in the next month is 0.355 to 3 decimal places.
- Find the probability of at least 2 breakdowns in each of the next 4 months.
The teachers would like a new photocopier. The head teacher agrees to monitor the situation for the next 12 months. The head teacher decides he will buy a new photocopier if there is more than 1 month when the photocopier has at least 2 breakdowns.
- Find the probability that the head teacher will buy a new photocopier.