Suppose approximately 80% of all marketing personnel are extroverts, whereas about 70% of all computer programmers are introverts. (Round your answers to three decimal places.) (a) At a meeting of 15 marketing personnel, what is the probability that 10 or more are extroverts?

Total probability = 0.939

Step-by-step explanation:

For this problem, we need to consider both probability and permutations.

Let's first calculate the probability of exactly 10 are extroverts in the meeting.

This can be achieved in the following way:

E-E-E-E-E-E-E-E-E-E-I-I-I-I-I

Here, E signifies and extrovert, while I signifies an introvert. These could be rearranged so as to create another type of a 10 - extrovert meeting. Thus lets calculate the probability for 10 extroverts in a specific order and multiply it with the different sequences the people can be picked out.

This is:

0.8^10 * 0.2^5 = 3.43 * 10^(-5)

The number of permutations for this event is: 15!/ (10! * 5!) = 3003

This is because we are dealing with similar objects, thus permutation equation stated is correct.

Total probability for 10 extroverts: 3.43 * 10^(-5) * 3003 = 0.103

Similarly, we can find out the probabilities for 11 , 12, 13, 14, and 15 extroverts.

These are:

11 extroverts: 0.1876

12 extroverts: 0.25

13 extroverts: 0.2309

14 extroverts: 0.1319

15 extroverts: 0.0352

Total Probability = above results (in bold) combined

Total Probability = 0.939

The method stated above is the basic implementation of the binomial theorem. The results are calculated the same way as using the binomial theorem does. They are explained separately in detail to make more sense.