# probability

Make a histogram showing the binomial probability distribution for the following: A waiter at the Green Spot resturant has learned from long experience that the probability that a lone diner will leave a tip is only 0.7. During one lunch hour he serves six people who are dining by themselves. (hint make table showing r= 0,1,2,3,4,5,6 and the p(r) that goes with each one ) What is the area of the bar graph showing r=3?

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1. prob(zero people leave tip) = C(6,0)(.7)^0 (.3)^6 = .000729
prob(1 person leaves tip) = C(6,1)(.7)(.3)^5 = .010206
prob(2 persons leave tip) = C(6,2)(.7)^2 (.3)^4
= .059535
prob(3 persons leave tip) = C(6,3)(.7)^3 (.3)^3
= .18522
prob(4 people leave tip) = C(6,4)(.7)^4 (.3)^2
= .324135
prob(5 people leave tip) = C(6,5) (.7)^5 (.3)
= .302529
prob(6 people leave tip = C(6,6) (.7)^6 (.3)^0
= .117649

note the sum of the above results = 1 , allowing for small round-off error

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posted by Reiny

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