1) A committee of size 5 is to be selected at random form 5 chemists and 3 mathe

Question

1) A committee of size 5 is to be selected at random form 5 chemists and 3 mathematicians.

a) Find a formula for the probability distribution of the number of mathematicians on the committee and find the probability of selecting exactly 2 mathematicians.

b) Find the expected value of the probability distribution in part a.

2) The number of people arriving for treatment at an emergency room can be modeled by a Poisson process with an average rate of 5 people per hour. What is the probability that exactly three arrivals occur during a particular hour? What is the probability of at most 4 arrivals in a given hour?

I need help with theses 2 questions please and thank you.

Explanation / Answer

Solution:-

2)

= 5

i) The probability that exactly three arrivals occur during a particular hour is 0.1404.

By applying Poisson probability:-

P(x; ) = (e-) (x) / x!

P(x = 3) = 0.1404

ii) The probability of at most 4 arrivals in a given hour is 0.441.

By applying Poisson probability:-

P(x; ) = (e-) (x) / x!

P(x < 4) = 0.441

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