The following represents the results of a survey in which individuals were asked to share what they perceive to be the ideal number of children.

a. What is the probability an individual believes the ideal number of children is 2?

b. What is the probability an individual is male and believes the ideal number o f children is 3?

c. Among the females, what’s the probability the individual believes the ideal number is 3?

d. What is the probability an individual believes the ideal number of children is at least 4?

Upon reviewing recent use of conference rooms at an engineering consulting firm, an industrial engineer determined the following probability distribution for the number of requests for a conference room per half-day: X 0 1 2 3 4 P(X=x) 0.07 0.15 0.45 0.25 0.08 a) Is this a legitimate probability distribution function? b) Currently, the building has two conference rooms. What is the probability that the number of requests will exceed the number of rooms for a given half-day? c) What is the probability that the two conference rooms will not be fully utilized on a given half-day? d) Obtain the mean, the standard deviation for the number of requests for conference rooms. e) Draw a probability histogram

Rolling a Die If a die is rolled one time, find these probabilities: a. Getting a 7 b. Getting an odd number c. Getting a number less than 7 d. Getting a prime number (2, 3, or 5)

4.Rolling a Die If a die is rolled one time, find these probabilities: a. Getting a number greater than 0. b. Getting a number greater than or equal to 3 c. Getting a number greater than 2 and an even number d. Getting a number less than 1

6.Riding to School The probability that John will drive to school is 0.37, the probability that he will ride with friends is 0.23, and the probability that his parents will take him is 0.4. He is not allowed to have passengers in the car when he is driving. What is the probability that John will have company on the way to school?

Roulette is one of the most common games played in gambling casinos in Las Vegas and elsewhere.

An American roulette wheel has slots marked with the numbers from 1 to 36 as well as 0 and 00 (the latter is called "double zero"). Half of the slots marked 1 to 36 are colored red and the other half are black. (The 0 and 00 are colored green.) With each spin of the wheel, the ball lands in one of these 38 slots.

One of the many possible roulette bets is to bet on the color of the slot that the ball will land on (red or black). If a player bets on red, he wins if the outcome is one of the 18 red outcomes, and he loses if the outcome is one of the 18 black outcomes or is 0 or 00. So, when betting on red, there are 18 outcomes in which the player wins and 20 outcomes in which the player loses. Therefore, when betting on red, the probability of winning is 18/38 and the probability of losing is 20/38.

When betting on red, the payout for a win is "1 to 1". This means that the player gets their original bet back PLUS and additional amount equaling their bet. In other words, they double their money. (Note: If the player loses they lose whatever amount of money they bet.)

Scenario 1: Mike goes to the casino with $400. His plan is to bet $100 on red 9 consecutive times or until he either has increased his total to $500 or has lost all of his money. What is the probability he will go bankrupt (i.e. end up with $0)? (Give your answer correct to four decimal places.)


(Hint: Set this problem up as an absorbing Markov Chain with 6 states where the states keep track of his current amount of money. The amount of money he has will always be $0, $100, $200, $300, $400, or $500. The states where he has $0 or $500 are absorbing states since he quits playing whenever one of these states is reached.


Scenario 2: Mike goes to the casino with $400 and will still be betting on red. As in Scenario 1, he will bet $100 each time he places a bet. However, instead of limiting himself to a maximum of 9 bets he decides to play indefinitely until he has reached $500 or goes bankrupt. If he uses this betting method, what is the probability he will eventually go bankrupt? (Give your answer correct to four decimal places.)

The purpose of this Question is to investigate some of the properties of the binomial probability distribution using Microsoft Excel. a. Suppose that for a binomial experiment with n = 15 trials, the probability of success is p = 0.10, and x is the number of successes. Obtain the probability distribution of x. Make a histogram for the probability distribution and comment on its shape. Find the mean and standard deviation of x. b. Suppose that for a binomial experiment with n = 15 trials, the probability of success is p = 0.50, and x is the number of successes. Obtain the probability distribution of x. Make a histogram for the probability distribution and comment on its shape. Find the mean and standard deviation of x. c. Which of the distributions in parts a–b had the greatest variability in the number of successes? Why does this make sense?

Three fair, six-sided dice colored red, green and blue are rolled. Calculate each of the following probabilities: (a) The probability all three dice show the same face (“triples”). (b) The probability that the red die shows a larger number than the green die. (c) The probability that the red die shows a larger number than the green die and the green die shows a larger number than the blue die. (d) The probability that the sum of the pips on all three dice is exactly 10. (e) The probability that the sum of the pips on all three dice is less than 10. (f) The probability that the sum of the pips on all three dice is greater than 10.

A Lab question asks whether the relationship between atomic number and electronegativity is direct, log, or inverse. I am inclined to say that it is direct since electronegativity increases with atomic number; though my out of my various graphs, the one graphing atomic number vs. log of electronegativity has the best line of fit (highest R^2) so I want to say it has a log relationship. Is this correct?

With a pressure of 0.4MPa, 2kg of water vapor is contained in a cylinder of 0.4m3, and the cylinder is connected to the piston. When keeping the pressure constant and raising the temperature of the water vapor by 300°CRkwl, calculate the amount of heat transfer from the water vapor to the water vapor.

Calculate the probability that the number 89 will come out when taking a ball from a bag with 120 balls numbered from 1 to 120.

Calculate the probability that "a number between 1 and 125" will come out when removing a ball from a bag with 130 balls numbered from 1 to 130.

If four questions with four options each are answered randomly, what is the probability of matching all of them?

Calculate the probability that "a number between 1 and 3" will come out when rolling a die.

If a die is rolled and the result is observed: What is the probability that a 6 does not come out?