Quantitative Methods Homework
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Here are three quantitative methods problems.
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Prob 1
Bill and Joe are playing a match in which the first player to win 2 games wins the match. For any given game, the probability that Bill wins is 1/3.
(a) Find the probability that Bill wins the match.
(b) What is the probability that the match takes only 2 games?
Prob 2
If the mean of a distribution is 100 and the standard deviation is 20, what is the range (+/- x) of the middle 3% of the population if we assume it is normal?
Prob 3
Demand (D) is often expressed as a function of price (P). Given the following demand curve, at what price will demand = 10?
D = 5000 - 25P - P^3
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Solution Summary
The expert examines quantitative methods in probability.
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PROBLEM 1
Here are the possible ways the match can turn out. B means that Bill won the game; J means that Joe won the game.
B B Bill wins in 2.
B J B Bill wins in 3
B J J Joe wins in 3.
J B B Bill wins in 3.
J J Joe wins in 2.
J B J Joe wins in 3.
Find the probabilities of each scenario by multiplying by 1/3 if Bill wins the game or by 2/3 if Joe wins.
B B Bill wins in 2. Probability: 1/3 * 1/3 0.1111
B J B Bill wins in 3 1/3 * 2/3 * 1/3 0.0741
B J J Joe wins in 3. 1/3 * 2/3 * 2/3 0.1481
J B B Bill wins in 3. 2/3 * 1/3 * 1/3 0.0741
J J Joe wins in 2. 2/3 * 2/3 0.4444
J B J Joe wins in 3. 2/3 * 1/3 * 2/3 0.1481
Notice that the probabilities add up to 1 (100%).
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