SOLUTION: 2. General Buck Twigidson is preparing to make his annual budget presentation to the U.S. senate and is speculating about his chances of getting all or part of his requested budget

Question 289489: 2. General Buck Twigidson is preparing to make his annual budget presentation to the U.S. senate and is speculating about his chances of getting all or part of his requested budget approved. From his 20 years of experience in making these requests, he has deduced that his chances of getting between 50 and 74 per cent of his budget approved are twice as good as those of getting between 75 and 99 per cent approved, and two and one-half times as good as those of getting between 25 and 49 per cent approved. Further, the general believes that there is no chance of less than 25 per cent of his budget being approved. Finally, the entire budget has been approved only once during the General's tenure and the General do not expect this pattern to change. What are the probabilities of 0-24 per cent, 25-49 per cent, 50-74 per cent, 75-99 per cent, and 100 per cent approval, according to the general?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
From his 20 years of experience in making these requests, he has deduced that his chances of getting between 50 and 74 per cent of his budget approved are twice as good as those of getting between 75 and 99 per cent approved, and two and one-half times as good as those of getting between 25 and 49 per cent approved. Further, the general believes that there is no chance of less than 25 per cent of his budget being approved. Finally, the entire budget has been approved only once during the General's tenure and the General does not expect this pattern to change.
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What are the probabilities of
a) 0-24 per cent,
b) 25-49 per cent,
c) 50-74 per cent,
d) 75-99 per cent,
e) 100 per cent
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Equations:
a + b + c + d + e = 1
c = 2d
c = 2.5b
a = 0
e = 0
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Substitute
0 + (2/5)c + c + (1/2)c + 0 = 1
Simplify:
(19/10)c = 1
c = 10/19
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Solve for d and b:
d = (1/2)c = 5/19
b = (2/5)c = 4/19
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Cheers,
Stan H.
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