You are in possession of a fake ID that gets you into a club 20% of the time. Ea

Question

You are in possession of a fake ID that gets you into a club 20% of the time. Each at- tempt is independent of other attempts. Let F denote the number of clubs that you fail to get into prior to getting into 2 clubs. How is F distributed?

1. Binomial (n = # of attempts, p = prob. of success)

2. A discrete random variable not listed.

3. Discrete Uniform { 1 , 2 , ..., n }

4. Negative Binomial ( r successes, p = prob . of success)

5. Geometric ( p = prob . of success)

6. Poisson ( = mean)

7. HyperGeometric ( n = size of group, B = number type I , G = number type II)

Explanation / Answer

from the given information probability of success is 0.20.

The random variable F denote the number of clubs that you fail to get into prior to getting into 2 clubs.

Hence F is distributed with

4. Negative Binomial ( r successes, p = prob . of success)

Since F is the number of failure untill getting 2 success. Hence this is a case of Negative Binomial

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