The two dams are identical with the exception that the water reservoir behind
dam A extends twice the horizontal distance behind it as that of dam B.
Which one of the following statements regarding these dams is correct?
A. The force exerted by the water on dam A is greater than that on dam B.
B. The force exerted by the water on dam B is greater than that on dam A.
C. Dam A is more likely to collapse than dam B if the water level rises.
D. Dam B is more likely to collapse than dam A if the water level rises.
E. The horizontal distance of the water behind the two...

1 answers and 12 views

Find the equilibrium vector for the transition matrix below
$$ \begin{bmatrix}0.4 & 0.4 & 0.2\\\\0.2 & 0.2 & 0.6 \\\\ 0.4 & 0.3 & 0.3\end{bmatrix} $$

1 answers and 13 views

Suppose Johnson Dry Cleaning (J) has a 40% market share initially, while NorthClean (N) has a 60% market share. Use the corresponding initial probability vector and the given weekly transition matrix to find the share of the market for each firm after each of the following time periods. Assume that customers bring in one batch of dry cleaning per week.
\begin{bmatrix}0.5 & 0.5\\\\0.65 & 0.35\end{bmatrix}
Row 1: J
Row 2: N
Col 1: J
Col 2: N
(a) 1 week
(b) 2 weeks
(c) 3 weeks
(d) 4 weeks

1 answers and 21 views

A small town has only two dry cleaners, Johnson and NorthClean. Each customer brings in one batch of clothes per week to one of these cleaners. The following transition matrix shows the probabilities that a customer initially using a particular dry cleaner will use a particular dry cleaner the next week.
$\begin{bmatrix}0.2 & 0.8\\\\0.65 & 0.35\end{bmatrix}$
Row 1: Johnson
Row 2: NorthClean
Col 1: Johnson
Col 2: NorthClean
Answer parts (a) through (e) based on this transition matrix.
(a) Find the probability that a customer initially bringing a batch of clothes to...

1 answers and 6 views

Suppose that a family has 3 children. Also, suppose that the probability of having a boy is 1/2. Find the probability that the family has at least 2 boys.

1 answers and 15 views

The chickens at Colonel Thompson's Ranch have a mean weight of 1850 g, with a standard deviation of 150 g. The weights of the chickens are closely approximated by a normal curve. Find the percent of all chickens having weights between 1606 g and 2288 g.

1 answers and 6 views

A company claims that 93% of its cereal boxes have at least as much cereal by weight as the amount stated on the box.
a. At a quality control checkpoint, one box out of a random sample of nine boxes falls short of its stated weight What is the probability of this happening due to chance variation in box weights?
b. Suppose three of nine boxes fail to have the claimed weight. What can be concluded? Explain.

1 answers and 14 views

The lifetime of a machine part has a continuous distribution on the interval (0, 60) with probability density function f, where f(x) is proportional to (10 + x) -2. Calculate the probability that the lifetime of the machine part is less than 21.

1 answers and 8 views

In a certain lottery, 6 white balls from a drum with 14 balls and 1 red ball from a dmm with 38 balls are selected. For a $2 ticket, players get one chance at winning the jackpot by matching all 7 numbers. Players win prizes when the numbers on their ticket match some or all of the numbers on the balls drawn (the order in which the balls are drawn does not matter). What is the probability of winning the jackpot by matching all numbers drawn?

1 answers and 29 views

What is the probability that at least 2 people have the same birthday in a group of 16 people? Assume that there are 365 days in a year.

1 answers and 6 views

In a certain Algebra and Trigonometry class, there are 18 freshmen and 26 sophomores. Of the 18 freshmen, 14 are male, and of the 26 sophomores, 20 are male. Find the probability that a randomly selected student is:
(a) A freshman or female
(b) A sophomore or male

1 answers and 5 views

Find the probability of the event P(A $\cup$ B) if P(A) = 0.23 , P(B) = 0.25, and P(A $\cap$ B) = 0.17.

2 answers and 8 views

Two fair dice are rolled. Determine the probability that the sum of the two dice is 6.

1 answers and 10 views

Determine the probability of having 5 boys in a 5-child family. Assume equally likely outcomes.

1 answers and 3 views

A coin is weighted so that tails is 5 times as likely as heads to occur. What probability should we assign to tails? to heads?

1 answers and 3 views

An urn contains 4 white balls and 5 red balls. Four balls are selected. In how many ways can the 4 balls be drawn from the total of 9 balls:
(a) If 3 balls are white and 1 is red?
(b) If all 4 balls are white?
(c) If all 4 balls are red?

1 answers and 3 views

How many different 12-letter words (real or imaginary) can be formed from the letters in the word TRIGONOMETRY?
There are __ different 12-letter words that can be formed

1 answers and 5 views

A student dance committee is to be formed consisting of 3 boys and 2 girls. If the membership is to be chosen from 8 boys and 7 girls, how many different committees are possible?
__ different committees are possible

1 answers and 3 views

In how many ways can 4 people each have different birthdays? Assume that there are 365 days in a year.
There are __ ways for 4 people to have different birthdays

1 answers and 3 views

How many arrangements of answers are possible for a true/false test with 9 questions?
There are __ possible arrangements

1 answers and 3 views

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