Hello,

Here are three quantitative methods problems.

Thanks!

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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 probabilitythat 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 meanof a distribution is 100 and the standard deviationis 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

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%).

Find the …

The expert examines quantitative methods in probability.