You are conducting a randomized clinical trial with four groups (arms).The four randomization groups are: (i) Arm 1, receive Drug A at a dose of 30 mg/d; (ii) Arm 2, receive Drug B at a dose of 10 mg/d; (iii) Arm 3, receive Drug B at a dose of 20 mg/d; (iv) Arm 4, receive placebo.The clinical trial is performed blinded (masked).A simple randomization scheme is used (no stratification, blocking, etc.) and all arms have an equal probability of being selected.

1. If the clinical trial enrolls 500 patients, how many patients are expected to receive placebo?

1. Patient identification numbers (IDs) are assigned consecutively. When the randomization code is broken, Patient ID 25 was randomized to Arm 1.Given that Patient ID 25 was in Arm 1, what is the probability that Patient ID 26 was in any Arm other than Arm 1?

1. What is the probability that 3 consecutive patients will receive Drug A?

1. If the clinical trial enrolls 80 patients, what is the probability that exactly 60 patients receive a drug (either Drug A or Drug B)?