# Tagged Questions

31 views

### Problem solving: Counting and probability

i am a little bad at probability, i'm studying to overcome this lack. Since i'm not with a tutor i need some help on the correct way to approach a basic probability problem. I would appreciate your ...
45 views

### Represent math problems as Markov chains [on hold]

The step by step that takes to solve a math problem (algebra, calculus, etc.) could be seen as a Markov chain? When solving a problem, the next math rule that you are going to apply only depends of ...
25 views

### Slicing through a cuboid containing spheres, how many are exposed to the surface and what is their combined volume

So I place spheres of radius chosen at random from a normal distribution of known mean and standard deviation in a cub or cuboid at random (not overlapping) until a known density of the entire cube is ...
24 views

### Die Probability Question + Basics of Conditional Probability

A die is rolled twice. What is the probability of observing: a) a four and a three P (obtaining a four and a three) or P(obtaining a three and a four) therefore P(obtaining a four)* P(obtaining a ...
35 views

### (What is the formula to find) What is the probability that the sum of the numbers on the tickets chosen is at least 7?

Senario: Box A contains four equal-sized tickets, numbered 1, 2, 3 ,4 Box B contains three tickets of the same size, numbered 4, 5, 6 An experiment consists of selecting one ticket from the box A ...
56 views

### what is wrong in my answer and what will be the correct solution for this probability question ?

A and B play a game where each is asked to select a number from 1 to 5. If the two numbers match, both of them win a prize. The probability that they will not win a prize in a single trial is - ...
51 views

### X and Y are independent random variables and their distributions are..

X and Y are independent random variables and their distributions are.. $P(X=1) = 0.1$ $P(X=2) = 0.2$ $P(X=3) = 0.3$ $P(X=4) = 0.4$ $P(Y=4) = 0.4$ $P(Y=2) = 0.3$ $P(Y=3) = 0.2$ $P(Y=4) = 0.1$ I ...
26 views

### $X$ and $Y$ are continuous $RVs$, such that$f(x,y) = 2, 0\leq x\leq 1, 0\leq y\leq 1, 0\leq x+y\leq 1$

X and Y are continuous RVs, such that $f(x,y) = 2, 0\leq x\leq 1, 0\leq y\leq 1, 0\leq x+y\leq 1$ I'm trying to find $P(x<1/2,y>1/2)$. So i'm integrating from $\dfrac{1}{2}$ to $1$ for $y$ ...
63 views

### Let $U$ be $~U [0,1]$and let $Y = U^{\frac{1}{2}}$

Let $U$ be $\sim \mathcal{U}[0,1]$ and let $Y = U^{1/2}$. I'm having trouble finding the $E(Y)$. How do I go about doing this?
39 views

### P(X>Y) Probability Double Integral

$f(x,y) = \frac{12}{7(x^2 + xy)}$ $0 \le x \le 1$ and $0 \le y \le 1$ I want to know the $P(X>Y)$. I believe the correct solution to this is integrating from 0 to 1 for dy and y to 1 for dx ...
21 views

### Uniform Spinner is spun twice..

A fair uniform spinner is spun twice, and the results V and W are noted. V and W are uniform RVs ∼U[0,1]. I'm trying to answer the question what is the joint pdf for V and W. I know that I have to ...
24 views

### Probability “average” understanding

This is more of a problem understanding probabilities than an actual question. In a game I am playing I can use a certain item to try to unlock different levels. The item will unlock a new level ...
32 views

### Ehrenfest's urns have been loaded with a total of 6 balls…

Ehrenfest's urns (two of them) have been loaded with a total of 6 balls. If the first urn now contains 1 ball, what is the probability that it will contain 2 balls after the next transition? My ...
32 views

### Probability - A trial consists of tossing a fair coin twice and noting H = number of heads observed…

A trial consists of tossing a fair coin twice and noting H = number of heads observed. What is the probability that if 5 trials are performed, we will note H=0 two times, H=1 one time, and H=2 two ...
53 views

### Concept of Probability in math first level

I am trying to teach myself the concepts of probability and I was wondering if this is correct. I am only 13 years old and did not learn this yet. I am just reading parts of a probability book to get ...
58 views

### Mean and Standard Deviation self thought problem

I am 13 years old trying to teach myself about standard deviation and was wondering how this problem would look like. I know I am young to be learning this but I was reading about this and got ...
47 views

### Confusing -Probabilities.!!

Ok so far what i understand is this lets say...Having to draw a card from 52card-deck its probability is of course 1/52.Now the probability to say that i will keep drawing this same card 10 times of ...
39 views

### Number of collisions of particles in a box. Application to epidemiology

I was surprised to see in this biology article a model assuming that the number of newly infected cells is a linear function of the number of (healthy) cells and of the number of viruses. I am not ...
30 views

### An organization was surveyed with regard to the number of children each member had…

I am studying for my exam and there is no solution for this question. Can anyone provide the correct answers? Thanks. An organization was surveyed with regard to the number of children each member ...
84 views

### Expected number of swaps required to get a palindrome out of a given string

Given a string, you keep swapping any two characters in the string randomly till the string becomes a palindrome. What is the expected number of swaps you will make? There will always be at least ...
29 views

### Probability problem regarding rooks on a chessboard

Eight rooks are placed in distinct squares of an 8 x 8 chessboard, with all possible replacements being equally likely. Find the probability that all the rooks are safe from one another.
34 views

### Deck of playing cards

Been going through an previous exam question and came across this: 5 cards are drawn from a deck of playing cards. What is the probability of drawing 3 aces? How do you calculate it using the C(n,r)? ...
30 views

### Maximum likelihood to throw exactly two 6s

One throws a dice $n$ times. For which value of $n$ is maximum the probability to obtain exactly two 6s? I get $$n=11 \text{ or } n=12.$$ My solution: the probability to obtain exactly two 6s in ...
79 views

### probability that a year has 53 mondays

We have the years from 2001, 2002, 2003,... to 2010. Say, a year is chosen at random from the listed years. What is the probability that the chosen year has 53 Mondays ?
24 views

### Calculating probabilities of events

Was going through past previous exam questions and came across this one: A manufacturer of lie detectors is testing its newest design. It asks 300 people to lie deliberately and another 500 people ...
40 views

### Two players $A,B$ throw two dice…

Two players $A,B$ throw two dice. A throw first, and they throw it in turns (i.e. $A,B,A,B,A...$). If $A$ gets sum of $10$ at the dice he wins, if $B$ gets $9$ - he wins. What is the probability ...
34 views

### Lifetime of exponential variable of a battery

Suppose that the operating lifetime of a certain type of battery is an exponential random variable with parameter $\theta=2$ $($measured in years$)$. Find the probability that a battery of this type ...
31 views

### Random variable of a store

The weekly profit in thousands of dollars of Miller's Office Supply Store is random variable X whose cdf is given as follows: $F(x)=0$ for $x<0$; $F(x)=(3/32)(2x^2-x^3/3)$ for $0 \leq x \leq 4$; ...
63 views

### The game of craps and dice

The game of craps involves the repeated tossing of a pair of dice. In the game of craps, Nancy throws a five on ther first tos of a pair of dice. ["Five" means that the sum of the number ofr dots on ...
37 views

### Combinations with multiple kids

In a certain country, it has been found over many years that $55$% of the babies born there are males. For a family in that country with five children, what is the probability that (i) the two ...
45 views

### Permutations of numbers

Given the five digits $1,3,4,6,$ and $7$. In the following question, it should be understood that repition of a digit is not allowed. (i) How many three-digit numbers can be formed from the ...
38 views

### Reputation probabilities

Is there a probabilistic model for what one's reputation can be on MSE? I can of course obtain increments of points in +2, +5, + 10, + 15, +50, +100. Are there models for what my reputation will ...
51 views

### Probability of World Series - Pascal and Fermat [closed]

In the World Series, each opponent attempts to win 4 of 7 games. In 1989, Oakland had already won the first two games as the San Francisco Giants and the Oakland Athletics were getting ready to play ...
154 views

### Puzzle - zero knowledge proof

I am solving the following problem : I have edge-matching puzzles, where all pieces are squares and the grid has $n$*$n$ format. There is no global image to guide a puzzle solver. Despite the puzzles ...
311 views

### Expected number of points on circle to form an acute angled triangle

This problem was asked to me in an interview. We keep on adding points on a circle uniformly until there exist three points on the circle which form an acute angled triangle. What is the expected ...
46 views

### conditional probability Pc(B)

I am looking for the probability of Pc(B) where the event of B={no two people are born in the same month} and event C= {exactly three people were born in the summer of june, july august} and there are ...
33 views

### probability of an event question

Find the probability of the event B= { NO two people are born in the same month}. There are 9 people involved by the way. Is it 1/12 * 1/11 * 1/10 * 1/9 * 1/8 * 1/7 * 1/6 * 1/5 * 1/4 * 1/3 * 1/2 * 1/1 ...
186 views

### Probability of two dice rolls

If two standard 6 sided dice are tossed what is the probability that a 3 is rolled on at least one of the two? How do I solve this without listing out the possibilities?
203 views

### Probability of winning the game 1-2-3-4-5-6-7-8-9-10-J-Q-K

A similar question to mine was answered here on stackexchange: Probability of winning the game "1-2-3" However, I am unable to follow the formulas so perhaps someone could show the ...
85 views

### Generate a formula for x in my case

Kindly see the following, ...
40 views

### Probability problem without replacement and series

I have a probability problem but I am unsure about the result. I would like to confirm my guesses. During an exam, 10 students are drawing one by one a question (among 12 questions) without putting ...
286 views

### Distributions of $X^2$ and $X-1$ when $X$ is geometric

Let$X$ be a discrete random variable with the probability mass function given by $p_x(x)= 2^{-x}$ for $x=1,2,3,\ldots$ and $0$ otherwise. a) Let $Y=X^2$, find the probability mass function of ...
63 views

### How to calculate the number of banner appearance based on monthly page views.

Hello fellow mathematicians. I have a website that gathers more then 44.000 page views per month. In my website I have 1 rotating place of 4 banner positions, each time it rotates 4 new banners will ...
45 views

### Confusion regarding probability of microbe producing everlasting colony.

My question is about the given solution to problem 4 in Newman's book 'A Problem Seminar'. Note that the book is available online at Springer. Problem 4 A microbe either splits into two perfect ...
44 views

This question is related to the equilibrium probability distribution of a markov chain. I have: $\vec {π} * \vec {P} = \vec {π}$ $[π_0,π_1,π_2,π_3]$ [ $\begin{matrix} 1/3 & 2/3 & 0 & ... 8answers 3k views ### Probability that a stick randomly broken in five places can form a tetrahedron Edit (March. 2014) This question has been moved to mathoverflow; see here. Randomly break a stick in five places. Question: What is the probability that the resulting six pieces can form a ... 0answers 59 views ### Define a problem using chernoff bounds We are preparing this for an exam. Given the division of a plane into a number of regions of different sizes. We would like to find, or guess, which is the biggest region, by doing the following. We ... 2answers 170 views ### Help solving probability problem! Can you help solve this problem? Place contains$N$coupons$(N>3)$.$3$tickets have prizes$ \$10000, \$1000, \$500$ respectively. $X$ is the number of coupons drawn before a prize-containing ...
Suppose that $a$ and $b$ are independently distributed random variables, with means; $\mu_a$, $\mu_b$ and variances; $\sigma_{a}^2$, $\sigma_b^2$, respectively. Further, let $c=ab + e$, where $e$ is ...