Question

A drug company conducts trials of a new vaccine for a rare but usually fatal disease. The company creates a

geometric model for this trial and establishes p=0.2 as the probability of success.
What can be said about this model?

Select all that apply.

1)The company predicts 4 failures before a success.

2)Each trial is independent.

3)The probability is the same for each trial.

4)The probability that the vaccine will be effective is p = 0.8.

5)Success is defined as preventing the disease.

6)The company predicts 8 failures before a success.

7)Success is defined as p = 0.2.​

Answer 1

What can be said about the model are;

1) The company predicts 4 failures before success

2) Each trial is independent

3) The probability is the same for each trial

4) Success is defined as preventing the disease

Explanation:

The probability of success for the vaccine, p = 0.2

Therefore, the probability that the vaccine is effective and prevents the disease = 0.2

A geometric distribution probability of success is given by the following formula;

P(X = x) = p × q⁽ˣ⁻¹⁾

The expected value, E(Y) = 1/p

The number of failures before success, E(Y) = (1 - p)/p = (1 - 0.2)/0.2 = 4

Where;

q = The probability of a trial failing = 1 - p = 1 - 0.2 = 0.8

q = 1 - p

∴ The e

The geometric model criteria are;

a) Each trial can only have one of two outcomes success or failure

b) The probability of success for each trial is fixed

c) The geometric distribution is concerned with finding how many trials are required to get one success

d) The trials are independent

Therefore, we have;

The number of failures the company predicts before a success = 4 failures

2) The trials are independent

3) Each trial has an equal probability

4) Success is defined by the effectiveness of the vaccine in the prevention of the disease