Linked Questions

52
votes
1answer
7k views

On average, how many friends would I need to have to have at least one friend's birthday every day? [duplicate]

I know that because of the birthday problem, even after 365 friends, you're going to have a lot of doubles and that there's also an infinitesimal chance that even with infinite friends that there's ...
6
votes
2answers
602 views

How many throws of a die until every possible result is obtained? [duplicate]

A die is thrown until every possible result (i.e., every integer from 1 to 6) is obtained. Find the expected value of the number of throws. How do I do that? I understand that probability for the ...
1
vote
1answer
7k views

How do you calculate probability of rolling all faces of a die after n number of rolls? [duplicate]

Possible Duplicate: Expected time to roll all 1 through 6 on a die Probability of picking all elements in a set Im pretty new to the stackexchange, and posted this is statistics, and then ...
6
votes
1answer
1k views

How many random samples needed to pick all elements of set? [duplicate]

If repeatedly picking a random element from a set, what is the expected number of times I'd have to pick before seeing all the elements of the set? Edit: when picking an element, it is simply counted ...
2
votes
3answers
2k views

How many papers do you expect to hand in before you receive each possible grade at least once? [duplicate]

A particular professor is known for his arbitrary grading policies. Each paper receives a grade from the set {A, A-, B+, B, B-, C+}, with equal probability, independently of other papers. How many ...
3
votes
2answers
2k views

How do wer find this expected value? [duplicate]

I'm just a little confused on this. I'm pretty sure that I need to use indicators for this but I'm not sure how I find the probability. The question goes like this: A company puts five different ...
1
vote
2answers
2k views

throwing a dice repeatedly so that each side appear once. [duplicate]

Pratt is given a fair die. He repeatedly throw the die until he get at least each number (1 to 6). Define the random variable $X$ to be the total number of trials that pratt throws the die. or ...
2
votes
1answer
1k views

Coupon Collector's Problem with X amount of coupons already collected. [duplicate]

I am having an issue with understanding how to calculate a specific case of the Coupon Collector's Problem. Say I have a set of 198 coupons. I learned how to find the estimated amount of draws to see ...
1
vote
1answer
815 views

Expected number of rolls to get all 6 numbers of a die [duplicate]

I've been thinking about this for a while but don't know how to go about obtaining the answer. Find the expectation of the times of rolls if u want to get all 6 numbers when rolling a 6 sided die. ...
3
votes
2answers
179 views

Expected value from popping bubbles [duplicate]

This is a fairly simple math problem from a programming challenge but I'm having trouble wrapping my head around it. What follows is a paraphrase of the problem: ...
2
votes
2answers
316 views

How many times must you roll a die until each side has appeared? [duplicate]

Let $X$ be the random variable which denotes the number of times a die has been rolled till each side has appeared. The order does not matter. We are trying to find $E[X]$. Let $X_i$ be a random ...
1
vote
1answer
390 views

How many iterations does it take to cover a range with random values? [duplicate]

Let's say I have a random number generator that generates integers uniformly from 0 to n-1 (where n is some positive integer). What is the expected number of iterations after which all the values 0..n-...
2
votes
1answer
470 views

calculating expected number of packets. [duplicate]

To go with the Lego Movie, Lego sell minifigures of the characters from the movie. They are sold in packets, where each packet contains one minifigure, and from the outside of the packet it is ...
1
vote
1answer
302 views

Expected number of trials until completion [duplicate]

You've got a discrete uniform distribution - what is the expected number of trials until each point is hit at least once? I started my thinking with maybe a Geometric distribution representing each ...
1
vote
1answer
372 views

Calculate expected value [duplicate]

Possible Duplicate: Expected time to roll all 1 through 6 on a die A question about Poker (and probability in general) Given a N-sided unbiased die. What is the expected number of throws of die ...
1
vote
1answer
204 views

Problem about number of trials until first success [duplicate]

The problem is like this: A standard deck contains $52$ cards, $4$ each of $2,3,4,5,6,7,8,9,J,Q,K,A$. Now start the following process. Pick a random card from the deck, show it, and then return it to ...
2
votes
1answer
122 views

Average number of stickers to complete an album [duplicate]

Suppose I have a sticker album which consists of $N$ stickers. How many stickers should I buy in average to complete this album, assuming all the stickers appear with the same frequency? More ...
1
vote
0answers
119 views

Expected values of Cereal box - Linearity of expectation puzzle [duplicate]

A toy is randomly put in a given Cereal box as a promotional gift. There can be N different types of toys and each one can be of any type N (IID). (a) Find the expected number of cereal box one has to ...
0
votes
1answer
77 views

If I'm sampling from N items, how many samples are needed to get all N items at least once? [duplicate]

I have a situation where I have N items in the population (e.g. these are item IDs in some inventory). Suppose I can sample and get back 1 item at a time, where each item has an independent and ...
4
votes
2answers
56 views

What is the probability distribution for this question? [duplicate]

I tried to find the probability distribution for this problem and then calculate the expectation of $n$. I suppose the total states of our problem would be $52^n$ and our desired states would be $52$ ...
-1
votes
1answer
84 views

Average # of tracks that must be heard on a CD, whose player's shuffle function can play the same song >1×, before all tracks of CD heard. [duplicate]

Suppose you have a CD of $n$ tracks. Your CD player's shuffle function is broken; it selects a random song, possibly even the one(s) already played, before all tracks are played. How many tracks (...
0
votes
0answers
84 views

4 Distinct toys in cereal boxes, on average, how many do I need to open to get all the toys? [duplicate]

here's my question: There are 4 distinct toys in cereal boxes, and each type, independent of prior selections, is equally likely to be in a box. On average, how many cereal boxes would you need to ...
1
vote
1answer
108 views

Random but very interesting probability question! [duplicate]

There are 100 types of cards, each type with a number from 1 to 100 on it. Each minute I am given a random card. Random means that the number of my card has an equal chance of being 1,2,3,...,100. I ...
0
votes
1answer
78 views

$x_1,x_2,\dots,x_n$ are i.i.d RVs uniformly distributed on $\{1,2,\dots,N\}$. [duplicate]

Let $x_1,x_2,\dots,x_n$ be independent identically distributed random variables uniform on $\{1,2,\dots,N\}$, and let: $Y_n:=\text{the number of different elements in } \{x_1,x_2,\dots,x_n\}$. Let $T:...
0
votes
0answers
63 views

Taking balls from a bag with replacement [duplicate]

Possible Duplicate: Expected time to roll all 1 through 6 on a die This is not a homework question. This question is spurred by me thinking about card collecting games (maybe baseball cards, ...
3
votes
0answers
58 views

Expected number of rolls until all die faces have appeared? [duplicate]

Suppose you have a die. On average, how many rolls does it take for all the faces (1 through 6) to have appeared? Also, what kind of distribution is this? (I thought of this question when watching ...
2
votes
1answer
41 views

Find expectation of a probablity distribution [duplicate]

There're k balls in a bag, each one with a different colour. Draw one ball from the bag randomly each time, then put the ball back. Let random variable X = the number of balls to draw until all k ...
1
vote
0answers
46 views

Probability: finding the expectation of “overlapping events” [duplicate]

Suppose there are 666 coins with 6 different colors in a non-transparent box. 111 of them are white coins. 111 of them are black coins. 111 of them are yellow coins. 111 of them are red coins. 111 of ...
1
vote
1answer
35 views

Expected time to fill a table [duplicate]

Say I have a table of numbers 1-6. I throw a 6 sided die a number of times. Each time I get a number I have not already had, I mark it in the table. What is the expected number of times to throw the ...
0
votes
0answers
35 views

How many rolls of an n-sided die before all n values are seen? [duplicate]

I'm currently playing a mobile game where one of the main activities is to collect characters from six different classes. You get new characters in the game by opening crystals, which each give you ...
1
vote
0answers
31 views

How many rolls of a $k$-sided dice should you expect to make before all numbers $1, 2,\dotsc, k$ have been seen at least once? [duplicate]

How many rolls of a $k$-sided dice should you expect to make before all numbers $1, 2,\dotsc, k$ have been seen at least once?
0
votes
0answers
28 views

Additional rolls to see all faces of a die [duplicate]

Suppose that a fair die is rolled repeatedly; different rolls are independent. N is the minimum number of rolls till each of the six faces of the die shows up at least once. Suppose that i ...
1
vote
0answers
28 views

Expected number of rolls to roll every number [duplicate]

If I am rolling I die until I roll every number at least once, what is the expected value of times that I will need to roll the die? After a brief computer simulation, I got 15. But why is this the ...
0
votes
0answers
26 views

Sum of geometric distributions [duplicate]

Imagine that I've got a big $N \times N$ boolean matrix (all entries are $0$ or $1$). At the beginning, the matrix is full of zeros. Then, I execute the following algorithm ...
0
votes
0answers
22 views

The expected number of n types of coupons have appeared at least once? [duplicate]

There are n different types of coupons and each item must contain one coupon. So what is the expected number of items needed to buy for all n types of coupons have appeared at least once?
0
votes
0answers
20 views

Expectation of the time that a person takes to be in every taxi in town [duplicate]

In a town there $n$ taxis. A person takes one of these taxis every day at random and with replacement. On average, how long does it take before he can claim that he has been in every take in the ...
0
votes
0answers
20 views

Expected number of tries before all elements of sample space have occurred. [duplicate]

We have a bag with 4 balls, one white, one black, one blue and one red. We are drawing balls with replacement. Find the expected value of the number of tries needed to draw all four colours. More ...
0
votes
0answers
20 views

Expected value of removing every ball once [duplicate]

I thought of this question and I somehow I can't figure out an answer Let there be a box with $n$ balls (which have numbers from $1$ to $n$ to that you can distinguish them). When we randomly pick a ...
1
vote
0answers
19 views

Expected minimum size of multinomial distribution that includes at least one value of each class [duplicate]

Suppose I have a vector and I include a new item on it at every time step. This item has one of $k$ different classes, each class has probability $\frac{1}{k}$ of being selected. Suppose now I stop ...
0
votes
0answers
18 views

Combinatorics and statistics question regarding drawing every element [duplicate]

Assuming a set of size X, on average how many attempts would it take to randomly draw every element in the set (returning it back after drawing)? I have a hard time formulating a title for this ...
0
votes
0answers
16 views

How many toys do I need to buy to get the whole set? [duplicate]

I'm collecting toys, they come in blind packs and there are 9 of them. Therefore for the first toy I have a 1.0 probability of getting a toy I haven't had before, then a 8/9, then a 7/9 and so on. On ...
0
votes
0answers
12 views

Calculating the number of trials to get all four outcomes [duplicate]

I was posed the following question recently: Suppose a brand of cereal has four different toys included in their cereal boxes, each with an equal probability of being found: On average, how many ...
11
votes
3answers
762 views

A question about Poker (and probability in general)

Okay, so I've been thinking about this question for a long time, and I'm starting to think that there isn't an answer. So please read the question, and if there is an answer, tell how you came to it, ...
17
votes
1answer
7k views

Probability distribution in the coupon collector's problem

I'm trying to solve the well known Coupon Collector's Problem by explicitly finding the probability distribution (so far all the methods I read involve using some sort of trick). However, I'm not ...
22
votes
3answers
695 views

How often was the most frequent coupon chosen?

In the coupon collector's problem, let $T_n$ denote the time of completion for a collection of $n$ coupons. At time $T_n$, each coupon $k$ has been collected $C_k^{n}\geqslant 1$ times. Consider how ...
2
votes
2answers
5k views

The coupon collectors problem [closed]

Each box of a certain breakfast cereal contains one of ten different coupons, each with the same probability. We win a prize if we manage to obtain a complete collection of all the different coupons. ...
3
votes
1answer
620 views

How long does it take to complete a sticker album?

We are collecing stickers in chocolate bars and whenever we open a bar we get a random new sticker. There are many different stickers and we try to collect them all. We open the first bar and get a ...
1
vote
4answers
115 views

Number of attempts to see all faces $1, 2, 3, …, 6$ when rolling a dice? [closed]

Recently I have been thinking about the following random experiment: we repeatedly roll a dice until we see all the faces $1, 2, 3, 4, 5, 6$ of the dice at least once. Let $X$ = number of attempts ...
3
votes
1answer
483 views

Expected number of rolls on a die until each face has appeared at least twice

Note: The die is fair, normal 1 - 6 die. So I understand that the expected number of rolls until each face occurs is 14.7 by the following post: Expected time to roll all 1 through 6 on a die but ...
4
votes
2answers
590 views

What is the probability of rolling $n$ dice until each side appears at least once?

We roll a die until each side appears at least once, then we stop. What is the probability of rolling exactly $n$ dice? I guess the answer is $$6-6\left(\dfrac{5}{6}\right)^n\;,$$ but this may ...

15 30 50 per page