Use the appropriate formulas to calculate the following probabilities.

A cancer research clinic recruits 10 patients from their patient pool. Suppose that the pool contains 30% stage II breast cancer patients.

1. What is the probability that no stage II breast cancer patients are selected?

2. What is the probability that 3 or fewer stage II breast cancer patients are selected?

3. What is the probability that less than 4 stage II breast cancer patients are selected?

4. What is the probability that 7 or more stage II breast cancer patients are selected?

Use the appropriate formulas to calculate the following probabilities.

You are an administrator in the maternity ward of a hospital. There are 2700 deliveries each year, meaning that 900 take place between midnight and 8am when you usually have fewer nursing staff on duty.

The average number of deliveries per night is 900/365 = 2.47.

Calculate the following to make sure you have enough staff working the midnight to 8am shift:

1. What is the probability of exactly 2 children being born in one night?

2. What is the probability of more than 5 children being born in one night?

3. What is the probability of 8 or more children being born in one night?

4. What is the probability of exactly 4 children being born over two nights?