# Probability calculations

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A small management consulting firm presents both written and oral proposals in an effort to get new consulting contracts. Records indicate that the probability distribution Pxy(x,y) of X = number of oral proposals in a week and Y = number of written proposals in that week is given by the following table:

Y

________________________________

x 0 1 2 3 4

0 .010 .015 .030 .075 .050

1 .020 .030 .045 .060 .040

2 .030 .045 .100 .045 .030

3 .040 .060 .045 .030 .020

4 .050 .075 .030 .015 .010

a. Find the probability that there are two oral proposals and two written proposals in a particular week.

b. Find the probability that there are exactly two oral proposals and two or fewer written proposals in a particular week.

c. Find the probability that there are two or fewer oral proposals and two or fewer written proposals in a particular week.

For many years TV executives used the guideline that 30 percent of the audience were

watching each of the prime-time networks and 10 percent were watching cable stations on

a weekday night. A random sample of 500 viewers in the Tampa-St. Petersburg, Florida,

area last Monday night showed that 165 homes were tuned in to the ABC affiliate, 140 to

the CBS affiliate, 125 to the NBC affiliate, and the remainder were viewing a cable station.

At the .05 significance level, can we conclude that the guideline is still reasonable?

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This solution gives the step by step method for computing probability from the given data.

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1. A small management consulting firm presents both written and oral proposals in an effort to get new consulting contracts. Records indicate that the probability distribution Pxy (x,y) of X = number of oral proposals in a week and Y = number of written proposals in that week is given by the following table:

Y

________________________________

X 0 1 2 3 4

0 .010 .015 .030 .075 .050

1 .020 .030 .045 .060 .040

2 .030 .045 .100 .045 ...

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