There are 100 students in a club. 20 are seniors. 12 arrive at December’s meeting at random. We want to predict the number of seniors that arrive. Describe the distribution and determine P(x=3).

A First Course in Probability (10th Edition)
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ISBN:9780134753119
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Chapter1: Combinatorial Analysis
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There are 100 students in a club. 20 are seniors. 12 arrive at December’s meeting at random. We want to predict the number of seniors that arrive. Describe the distribution and determine P(x=3).

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Step 1

The probability that a randomly selected senior will arrive in meeting will be

Probability homework question answer, step 1, image 1

As per the information senior attending the meeting will be independent of other seniors. As well there are only two possible outcomes that either the senior will attend the meeting or not attend the meeting. The probability that any randomly selected senior among 12 seniors attend the party is equal to 0.6 and it is constant for every senior.

 

So, the number of seniors that arrive will follow binomial distribution with parameters n = 20  and p = 0.6. 

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