6
votes
4answers
198 views

100 sequential parking spaces

In my high school's math club today, we explored but did not solve this interesting problem: 100 autonomous robotic vehicles enter a warehouse in arbitrary order to park. Inside the warehouse, there ...
2
votes
1answer
24 views

Distinct elements in the Union and Intersection of A and B

Take a set $x$ with $10$ distinct elements. Rule: Everytime you have two subsets, $A$ and $B,$ you also have $A\cup B$ and $A \cap B.$ What is the maximum number of subsets you can have such ...
0
votes
2answers
27 views

Lottery problem - Chance of 4 out of 5 balls matching?

In a lottery, an urn contains 40 balls that are numbered 1, 2, ..., 40. Each week, 5 balls are drawn from the urn without replacement. To enter, one chooses 5 numbers. Anyone who correctly predicts ...
1
vote
1answer
40 views

What to do when a probability problem becomes unwieldy to check via simulation?

I am assuming that some probability problems cannot be solved easily since there may be a lot of cases to handle and it would make miscounting likely. However, some problems do not simulate well on a ...
0
votes
1answer
55 views

What is the probability the best case occurs? (Comp Sci Type Question)

I'm having trouble figuring out what's the probability the best case occurs? It's my first time bringing together probabilistic knowledge into computer science. The question goes as such. Consider ...
1
vote
1answer
28 views

raBinomial distribution with dependent trials?

I need your help with following problem: String with n characters is given. For each character in string there is probability p that it is wrong. Now you take a sliding window of length k, k<= n, ...
2
votes
1answer
49 views

Coin-tossing games

Suppose that you start off with $100$ dollars. You toss a coin $10$ times and guess it right $5$ times and lose $5$ times (the order of the outcomes is not known). It is known that every time you ...
0
votes
4answers
69 views

Chance of playing a game

You are offered a chance to play a game. the rules are simple. there are $100$ cards face down. Of these, $55$ say win and $45$ say lose. You begin with $10000$ dollars. You must bet $1/2$ of your ...
0
votes
0answers
35 views

Conditional Probability - Order is important!

Probability that Mark wins a tennis match he plays is 0.8. A knockout tournament requires players to win 5 matches to win the tournament. What is the probability that Mark wins the tournament? ...
6
votes
2answers
476 views

Find the probability of winning at this lottery.

So, the problem I found goes like this: You have $n$ different numbers, numbered from $ 1 $ to $n$. You can randomly choose $m$ (different) of them. The computer also randomly selects $m$ ...
2
votes
1answer
30 views

Find some probabilities given the probability tree

i've been practicing probability since it's not my strength, but i am doing that without a tutor or an official course, just books and videos. I was reading a problem, and i was capable of draw the ...
1
vote
2answers
55 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 ...
1
vote
0answers
27 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 ...
0
votes
2answers
26 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 ...
1
vote
2answers
37 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 ...
1
vote
1answer
57 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 - ...
0
votes
2answers
53 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 ...
0
votes
1answer
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 $y$ ...
1
vote
3answers
72 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?
0
votes
1answer
57 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 ...
0
votes
1answer
23 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 ...
0
votes
1answer
25 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 ...
1
vote
1answer
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 ...
1
vote
1answer
33 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 ...
1
vote
2answers
64 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 ...
-1
votes
1answer
76 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 ...
3
votes
3answers
49 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 ...
0
votes
1answer
31 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 ...
0
votes
1answer
173 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 ...
0
votes
1answer
75 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.
0
votes
2answers
35 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)? ...
3
votes
1answer
32 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 ...
0
votes
1answer
90 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 ?
0
votes
1answer
26 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 ...
0
votes
1answer
43 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 ...
0
votes
1answer
39 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 ...
1
vote
1answer
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 $0 \leq x \leq 4$; ...
2
votes
3answers
74 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 ...
0
votes
1answer
39 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 ...
1
vote
3answers
50 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 ...
1
vote
0answers
45 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 ...
2
votes
0answers
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 ...
4
votes
0answers
164 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 ...
3
votes
2answers
336 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 ...
0
votes
1answer
48 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 ...
1
vote
0answers
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 ...
1
vote
1answer
198 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?
2
votes
3answers
216 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 ...
2
votes
1answer
95 views

Generate a formula for x in my case

Kindly see the following, ...
2
votes
1answer
42 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 ...