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