Questions
A coin has a probability of 1/4 for head, and is repeatedly tossed until we throw...

A coin has a probability of 1/4 for head, and is repeatedly tossed until
we throw head. The successive results of the toss are independent of each other.
What is the probability that the first time we throw head after an odd number of toss?
Hint: Use the law of total probability and consider the event that the
first toss is head is, and her complement, as conditioning events.

Correct answer: 3/7

In: Statistics and Probability

A survey has been conducted in canteen during the lunch time. The average number of customers...

A survey has been conducted in canteen during the lunch time. The average number of customers arrived in a 5-minute interval is 8.

a) What is the probability that exactly 3 customers will arrive in a 2-minute interval?

b) What is the probability that less than 3 customers will arrive in a 4-minute interval?

c) What is the probability that more than 1 customers will arrive in a 30-second interval?

In: Statistics and Probability

In a​ 22-year period, a particular location was hit by 38 major hurricanes. Assume that major...

In a​ 22-year period, a particular location was hit by 38 major hurricanes. Assume that major hurricanes are independent of each other and that the mean number of hurricanes per year has not changed.

​a) What's the probability of no hurricanes next​ year?

​b) What's the probability that during the next​ year, there is exactly one​ hurricane?

​c) What's the probability that during the next​ year, there is more than one​ hurricane?

In: Statistics and Probability

9.50. Each person in a group of twenty persons is assigned a random number from 1...

9.50. Each person in a group of twenty persons is assigned a random number from 1 to 100 (both included). It is possible for multiple persons to be assigned the same number, and all assignments are equally likely. What is the probability that at least two persons in the group share the same number?

In: Statistics and Probability

Consider a student with an ID number: 13762348. The student is going to select two digits...

Consider a student with an ID number: 13762348. The student is going to select two digits at random from the digits in the ID number, one after another and without replacement. What is the probability that the sum of the two digits is less than 10, given that the first digit is an odd number?

In: Statistics and Probability

Winning the jackpot in a particular lottery requires that you select the correct five numbers between...

Winning the jackpot in a particular lottery requires that you select the correct five numbers between 1 and 25 and, in a separate drawing, you must also select the correct single number between 1 and 37. Find the probability of winning the jackpot.

The probability of winning the jackpot is _____

In: Statistics and Probability

Write a C++ program that inputs two simplified poker hands (as defined in homework #5) and...


Write a C++ program that inputs two simplified poker hands (as defined in homework #5) and
determines which (if either) of the hands is the winner, according to the following rules:
• If the two hands have different types (3-of-kind, straight, pair, high-card), the hand with
the better type (i.e., appears earlier in this list) wins.
• If they have the same type, the higher significant card wins.
• If the hands have the same type and significant card, there is no winner (a tie).
• Note that the only significant factors are four types of hand and what is the significant
card (high card or card in a pair/triple). In real poker, a tie in the criteria above would be
resolved by comparing the non-pair or next-highest card. You may do this if you wish,
but it is not required
Further Assignment Parameters:
Your program should be decomposed into functions and files. You should not have more
than one function that does the same thing. For example, there should be one function
(with three reference parameters) that inputs a hand. This function can be used twice
(passing different cards as parameters) in order to input the two hands.
• You may start with your solution to homework 5, or you may start with my solution, or
you may start over. If you start with your solution, you should deal with any concerns
that I wrote on it when I graded it. Note that much of this homework involves
converting previous code into functions. There will be very little new code, most of
which will be involved with comparing two hands in order to select a winner.
• Use the existing tool functions from class lectures whenever you can!


***Below is homework #5 (already done):

In the output, cards will be described as follows:
• 2-10 are described by the words for their numeric values: two, three, etc.
• 1 is called an ace, 11 is called a jack, 12 is called a queen, and 13 is called a king.
The evaluation of a hand is based on the first of the following cases that matches the cards:
• All three cards are equal to each other.
Sample output for 4 4 4: You have three fours.
• The three cards form a straight (three successive values).
Sample output for 68 7: You have an eight-high straight.
• Two cards (a pair) are equal.
Sample output for 6 3 6: You have a pair of sixes.
• Whatever is the highest card.
Sample output for 11 18: You have a jack.
I recommend sorting the card values before trying to evaluate the hand - that makes it much
easier. Also, work on one thing at a time: first determine what kind of hand (3 of kind, 2 of kind,
straight....) and then determine what is the "significant" card for that hand (it becomes very
messy and exhausting if you try to do both at the same time!). Check for card values being
equal to each other (card1 == card2), not specific values (card1 == 1 && card2 == 1 || card1 ==
2 && card 2 == 2 || ...). If you check each value, your program will be hundreds of lines long!

In: Computer Science

The City of Chicago has to select a representative from the city council to go to...

The City of Chicago has to select a representative from the city council to go to an economic development conference. It will also select an alternate representative, in case there is a conflict or emergency that prevents the representative from attending. City policy says that these selections are to be made completely at random from the members of the city council. The council’s membership is made up of 7 Democrats and 5 Republicans. I'm interested in the political party affiliation (Democrat or Republican) of the two selected people.

Show all work-

1. Summarize these trials of selecting two people (representative and alternate representative) from the city council in a Probability Tree.

2. Construct a discrete probability distribution for the number of Democrats among the two selections. Make sure that you include all the properties of the discrete probability distribution.

3. From the discrete probability distribution, calculate the mean and standard deviation of the number of Democrats.

In: Statistics and Probability

Sam is writing a research paper for his graduation. On his draft of the paper, there...

Sam is writing a research paper for his graduation. On his draft of the paper, there are an average of 5 typos on each page. Assume each typo is independent.

a) Let Y to be the number of typos in Chapter 1, which is 4 full pages in length. What is the probability that there are 18 typos in the first chapter? What is the distribution, parameter(s), and support of Y?

b) What is the probability that Sam has 18 to 20 typos (inclusive) in the draft of Chapter 1?

c) What is the expected value and variance of Y?

d) What is the probability that Sam has 10 typos in Chapter 1 and 10 typos in Chapter 8 (which is 5 pages)?

e) It turns out that the first 4 chapters have the same number of pages (4 pages), what is the probability that Sam has 18 to 20 typos (inclusive) in 2 of the 4 chapters of his draft?

In: Statistics and Probability

3. The number of book-case units ordered in any one month varies between 100 and 1400...

3. The number of book-case units ordered in any one month varies between 100 and 1400 units, as per the probability model that is found in the associated RegINdust.csv file. Only the first 6 entries of this probability model are shown below (See associated file for full model). X PrX 100 0.3316 300 0.2558 650 0.0920 800 0.1620 850 0.1412 1050 0.0149 Table 1: First 6 entries of the probability model circumscribing the number of units of book-cases that will be demanded per month. Caution for the full model please consult the RegIndust.csv file.

(a) (1 point) Is the full probability model proper ? Justify your answer.

(b) (1 point) Please determine the expected value for X

(c) (2 points) Determine the standard deviation for X.

(d) (1 point) Determine the coefficient of variation for X

In: Statistics and Probability