Question

Q3. A or B?

A pharmaceutical company is testing two new medication that alleviates rheumatism symptoms. 35 random patients tested drug A and 71% of them reported their symptoms are alleviated. 60 random patients (who are different from patients who tried drug A) tried drug B and 73% of them reported they felt better after taking the medication. Suppose, the pharmaceutical company would launch an advertising campaign if more then 70% of the patients report the medication is effective.

1. What is the probability that drug A will be launched in the advertising campaign? (4 points)
2. What is the probability that drug B will be launched in the advertising campaign? (4 points)
3. What assumptions did you make to do the calculations? ( 2 points)

Answer 1

a)

Let the random variable X is the number of patients reported their symptoms are alleviated.

The number of patients reported their symptoms are alleviated will have a binomial distribution with parameter n and p. The distribution can be represented as;

Now, the required probability for more than 70% reported their symptoms are alleviated (70% of n=35 is 24.5 i.e. 25),

For calculation purpose, the probability is obtained in excel using the function =1-BINOM.DIST(24,35,0.71,TRUE).

b)

Let the random variable X is the number of patients reported they felt better after taking the medication.

The number of patients reported they felt better after taking the medication will have a binomial distribution with parameter n and p. The distribution can be represented as;

Now, the required probability for more than 70% reported their symptoms are alleviated (70% of n=60 is 42),

For calculation purpose, the probability is obtained in excel using the function =1-BINOM.DIST(42,60,0.73,TRUE).

c)

Here we take an assumption that the each trial has only two outcome and each outcome has the same probability of success.