Question

A clinic tests patients for the novel Zombie virus. A patient is likely to be tested positive with probability 0.25. If each patient testing is independent, answer the questions below:

1. What is the probability that the 6th patient is tested positive?

2. What is the probability that the 6th patient is the first one to be tested positive? Use an appropriate random variable family and the provide a PMF.

Answer 1

1. What is the probability that the 6th patient is tested positive?

we are given that A patient is likely to be tested positive with probability 0.25.

Hence for any nth patient the probability patient to be tested positive is 0.25

which means the probability that the 6th patient is tested positive is 0.25.

2. What is the probability that the 6th patient is the first one to be tested positive? Use an appropriate random variable family and provide a PMF.

The geometric probability is a type of discrete probability distribution X that can take random values on the range of [1,+∞).

The random variable X is the number of trials required to get the first successes.

For a value x in x∈[1,+∞), the geometric probability is computed as follows:

The following information is provided:

The population proportion of success is p = 0.25, also, 1 - p = 1 - 0.25 = 0.75.

We need to compute Pr(X=6)

This implies that

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