Consider a best-of-seven series. Two teams A and B play one another until one of the teams wins 4 games. The games are played indepedently, and the probability of team A winning any game is 2/3.

a. Find the expected number of games the series lasts.

b. Find the expected number of games team A wins.

c. Find the expected number of games team B wins.

d. Find the probability of team B winning the series.

Problem 5 (6 pts). A and B play a series of games. Each game is independently won by A with probability p and by B with probability 1 − p. They stop when the total number of wins of one of the players is two greater than that of the other player. The player with the grater number of total wins is declared the winner of the series. Find the probability that a total of 4 games are played.

2) An Elevator with a mass of 2500 Kg rests at a level 10 m above the base of an elevator shaft. It is raised to 100 m above the base of shaft, where the cable holding it breaks. The elevator falls freely to the base of the shaft and strikes a strong spring. The spring is designed to bring the elevator to rest and to hold the elevator at the position of maximum spring compression. Assuming the entire process to be frictionless, calculate:

a) The potential energy of the elevator in its position relative to the base of the shaft.

b) The work done in raising the elevator.

c) The potential energy of the elevator in its highest position relative to the base of the shaft.

d) The velocity and kinetic energy of the elevator just before it strikes the spring.

e) The potential energy of the compressed spring.

334423. #1: Write a program that optionally accepts an address and a port from the command line. If there is no address/port on the command line, it should create a TCP socket and print the address (i.e. server mode). If there is an address/port, it should connect to it (i.e. client mode). Once the connections are set up, each side should enter a loop of receive, print what it received, then send a message. The message should be “ping” from the client and “pong” from the server.

Hints:

You will need to pick a port for the server – something over 1024.

Ensure that you open your firewall to let the signal through.

1) A system of particles is known to have a total kinetic energy of zero. What can you say about the total momentum of the system?

(2) A bowling ball and a Ping-Pong ball are rolling toward you with the same momentum. If you exert the same force to stop each one, which takes a longer time to bring to rest?

(3) A cannon sits on a stationary railroad flatcar with a total mass of 1000 kg. When a 10-kgcannonball is fired to the left at a speed of 50 m/s, what is the recoil speed of the flatcar?

please explain and answer all 3

NOTE: Answers using z-scores rounded to 3 (or more) decimal places will work for this problem.

The population of weights for men attending a local health club is normally distributed with a mean of 179-lbs and a standard deviation of 29-lbs. An elevator in the health club is limited to 34 occupants, but it will be overloaded if the total weight is in excess of 6460-lbs.

Assume that there are 34 men in the elevator. What is the average weight beyond which the elevator would be considered overloaded?
average weight = lbs

What is the probability that one randomly selected male health club member will exceed this weight?
P(one man exceeds) =
(Report answer accurate to 4 decimal places.)

If we assume that 34 male occupants in the elevator are the result of a random selection, find the probability that the evelator will be overloaded?
P(elevator overloaded) =
(Report answer accurate to 4 decimal places.)

If the evelator is full (on average) 2 times a day, how many times will the evelator be overloaded in one (non-leap) year?
number of times overloaded =
(Report answer rounded to the nearest whole number.)

Is there reason for concern?

• yes, the current overload limit is not adequate to insure the safey of the passengers
• no, the current overload limit is adequate to insure the safety of the passengers

A cylinder with a movable piston is filled at 24^oC with a gas that occupies 36.2cm³. If the maximum capacity of the cylinder is 65.2cm³, what is the highest temperature to which the cylinder can be heated at constant pressure without having the piston come out?

Game of dice - fair dice:

If I throw a number >= 5 I win. If he throws a number =< 4 he wins.

I throw the first dice.

Given that he loses(throws a number >4) what is the probability of me winning ?

What is the expected number of throws before either of us wins?

Alice and Bob play the following game. They toss 5 fair coins. If all tosses are Heads, Bob wins. If the number of Heads tosses is zero or one, Alice wins.

Otherwise, they repeat, tossing five coins on each round, until the game is decided.

(a) Compute the expected number of coin tosses needed to decide the game.

(b) Compute the probability that Alice wins

An elevator has a placard stating that the maximum capacity is 2520 lblong dash15 passengers.​ So, 15 adult male passengers can have a mean weight of up to 2520 divided by 15 equals 168 pounds. If the elevator is loaded with 15 adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than 168 lb.​ (Assume that weights of males are normally distributed with a mean of 175 lb and a standard deviation of 31 lb​.) Does this elevator appear to be​ safe?

The probability the elevator is overloaded is?

Does this elevator appear to be​ safe?