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I. In a certain type of conspiracy, the probability of a conspirator "talking" is 0.05, and the conspiracy will be considered "blown open" if at least five people "talk". Find the probability of the following conspiracies being "blown open" if they consist of

(a) 15 people (b) 20 people (c) 50 people (d) 100 people (e) 200 people (f) 400 people (g) 800 people


TS Contributor
This is a situation that may be modeled using the binomial distribution. Notice that you are asked: What is the probability that >= 5 conspirators will talk. So , if you interrogate 15 conspirators, you want to know the probability that 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, or 15 conspirators talk. Which is also the same as:

1- P(0, 1, 2, 3, or 4 conspirators will talk out of 15)

In this case, we will want to sum the probabilities associated with each possibility to determine the final probability.