1-

Two coins are flipped, followed by rolling a die as many times as the number
of heads shown.
(a) What is the probability of getting fewer than 5 dots in total?
(b) Given that there were exactly 3 dots in total, what is the conditional
probability that the coins showed exactly one head?

2-

Four people are dealt 13 cards each. You (one of the players) got one ace.
What is the probability that your partner has the other three aces?

3-

Two shooters are shooting two shots each at a target. The probability of the
event “the first shooter hits the target” is 0.7 for each shot and the probability for
the second shooter is 0.8. What is the probability of both shooters missing the
target?

4-

Suppose the experiment consists of rolling two dice (red and green), the event
A is: “the total number of dots equals 6”, B is: “the red die shows an even number”.
Compute P(B/A).

3. Binomial Distribution: A real estate agent has ten properties that she shows. She feels that there is a 10% chance of selling any one property during a week. The chance of selling any one property is independent of selling another property.

1. Compute the expected number of properties to be sold in a week.
2. Compute the standard deviation of the number of properties sold each week.
3. Compute the probability of selling five properties in one week.
4. Compute the probability of selling at least three properties in one week.

4. Poisson Distribution: It has been reported that U.S airlines average about 1.6 fatalities per month. Assume that the probability distribution for x = the number of fatalities per month, can be approximated by a Poisson probability distribution.

1. What is the probability that no fatalities will occur during any given month?
2. What is the probability that one fatality will occur during any given month?
3. Find the expected value of x
4. Find the standard deviation of x.

1)

a. There is an elevator on the 102th floor of the Empire State Building with a sign: MAXIMUM WEIGHT 2900 LBS. During refurbishment, the cable was being replaced. A section of the new cable is cut up and tested for its breaking strength. The cable was tested 20 times and the average breaking point of the sample was found to be 3100 LBS with a standard deviation of 280 LBS. Construct an appropriate hypothesis test that determines whether the cable is safe to use. Since this cable has lives on the line (literally) use an alpha level of .005. Show all work! (Hint: Do you desire the actual breaking point is greater or less than 2900 LBS?)

b. In a hypothesis test, what does the p-value mean? Hint: What does it mean in terms of the sample that was drawn?

Gases A₂ and B₂ react according to the equation: A₂ + B₂ → A_xB_y . If equimolar ( not necessarily stoichiometrically equivalent) quantities are placed in a reaction vessel with a massless, frictionless piston and allowed to react to completion. The density of the gas mixture after reaction is 1.5X the original density. Find the empirical formula? Is there only one possibility? Explain.

Thermodynamics

An insulated piston/cylinder device contains ideal CO2 gas at 800 kPa, 300 K, which is then compressed to 6 MPa in a reversible adiabatic process. Determine the final temperature and the specific work during the compression process using:

(a) Ideal gas tables A.8,

(b) Constant specific heats A.5.

The volume of 1 kg of helium in a piston-cylinder device is initially 7 m3 . Now helium is compressed to 3 m3 while its pressure is maintained constant at 150 kPa. Determine the initial and final temperatures of helium as well as the work required to compress it, in kJ. You may assume deal gas behavior.

A cylinder with a movable piston contains 2.00 g of helium, He, at room temperature. More helium was added to the cylinder and the volume was adjusted so that the gas pressure remained the same. How many grams of helium were added to the cylinder if the volume was changed from 2.00 L to 3.50 L ? (The temperature was held constant.)

A 10 kg steam initially at 2 MPa saturated vapor is inside an insulated piston cylinder. The cylinder has a bottom valve. As this valve opens, steam at 800 kPa and 200C exits while the steam inside the tank has 400kPa saturated vapor. Find the exit mass of steam from the cylinder in kg.

A doughnut contains about 302 Calories. (Note: These are "food" Calories.) After eating this doughnut, you decide to compensate by taking the stairs instead of using the elevator. If each stair has a height of 22 cm, how many stairs must you climb to compensate for the doughnut? Assume all the energy in the doughnut can be converted to mechanical energy. (Take 75 kg as the mass of a typical person.)

A doughnut contains about 280 Calories. (Note: These are "food" Calories.) After eating this doughnut, you decide to compensate by taking the stairs instead of using the elevator. If each stair has a height of 18 cm, how many stairs must you climb to compensate for the doughnut? Assume all the energy in the doughnut can be converted to mechanical energy. (Take 75 kg as the mass of a typical person.)