1. In the city of Greater Longley, COVID testing revealed that 3% of the population were infected with the COVID virus. Of those who had the virus 80% displayed symptoms (fever, dry cough and/or tiredness). Of those that did not have the virus, only 10% showed the same symptoms.
3. Determinethe probability that a randomly selected citizen of Greater Longley will display symptoms (fever, dry cough and/or tiredness).
4. Given that a person has the symptoms of fever, dry cough and/or tirednessdeterminethe probability that they have COVID.

1. An insurance company is considering developing a new product called Covid-Insurance, with the following benefits:

• If you catch Covid during the year and die your family will receive at $200,000 payout.
• If you catch Covid during the year and are hospitalised you will receive a $2000 pay out.
• If you don't catch Covid during the year OR if you catch it but are not hospitalised you will receive no payout.

The probabilities of these events are thought to be 0.0005, 0.002 and 0.9975 respectively.

1. Determineexpected annual payout per customer.
2. If it costs the insurance company $100 to process each payout,determinethe minimum annual premium the insurance company could consider charging for this policy.

1. Over the last 14 days, the number of new cases which require a ventilator has been:

2

1

2

3

2

1

0

1

2

1

2

2

3

1

1. Determinethe average number of new cases per day requiring a ventilator.
2. Explainwhich sort of distribution you might expect the number of new ventilator cases to follow.
3. If the hospital starts the day with three (3) free ventilators,what is the probabilitythey don't have enough to cater for the day's demand.

1. A COVID testing centre has the capacity to carry out 70 tests in a day. Only 90% of people who book a COVID test actually show up for the test. As a result the centre is considering "overbooking" and taking 75 bookings per day.
2. Explainwhat distribution you would think would apply to the daily number of people with a booking who show up for a test.
3. If they take 75 bookings,determinethe probability that more people show up in a day than the testing centre can handle.
4. A quick check of today's bookings reveals that 48 of the bookings are for 24 married couples. When married couples book, it is very unusual for just one to show up. (Either they both come, or they both miss the booking).Explainwhether this observation might affect your answer to part (ii).