1.There are 10 occupied hospital beds in the cardiac unit. In any hour, the probability that a patient in the unit is discharged is 0.05. The number of patients currently waiting (in various parts of the hospital) to occupy a bed in this unit is 3. The rate of new bed requests (coming from the emergency room) for this unit is on average 2 per hour and is Poisson distributed. What is the probability that the queue size decreases in the next hour?

2. A distribution facility has 100 SD cards in stock. 30 of these SD cards are low storage cards while the remaining 70 SD cards provide high storage. A camera company places an order for 20 high storage SD cards. However, there is a mistake at the distribution company and the camera company is sent 20 SD cards in a completely random fashion, so that any particular subset of size 20 has the same chance of being selected as any other subset. The camera company receives the shipment and randomly samples 5 of the SD cards for quality control purposes. What is the probability that the camera company will discover the mistake?