Question

A survey on the company's offering stock options was conducted by the Segal Company of New York.  

The data summary is presented below.

		Large Company	Small Company
Stock	Yes	30	50	80
Options	No	150	170	320
		180	220	400

a.     If a company is selected at random, what is the probability that the company offers stock options to their board members?

b.         If it is known that the company offeers stock options, what is the probability of this company being a large company?

c.  What is the probability of getting a large company or company that offers stock options?                   

d.         Does it matter if a company is large or small for offering stock options?

e.         The average rate of scoring in a game is 2 runs per minute. What is the probability that not more than 2 runs will be scored in the next one minute? Just 3 runs?                   

Answer 1

a)

probability that the company offers stock options to their board members =80/400=0.2

b)

P(large |stock options) =30/80=0.375

c) probability of getting a large company or company that offers stock options =(180+80-30)/400 =0.575

d)

Yes as P(large )=180/400 =0.45 is not equal to P(large |stock options) , therefore events are not independent,

e)

probability that not more than 2 runs will be scored in the next one minute

=P(X<=2)= P(X=0)+P(X=1)+P(X=2)=e^-2*2⁰/0!+e^-2*2¹/1!+e^-2*2²/2! =0.6767

P( Just 3 runs ) =P(X=3)=e^-2*2³/3! =0.1804