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 ...
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 ...
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 ...
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, ...
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 ...
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 ...
4
votes
1answer
133 views

How many correct answers does it take to fill the Trivial Pursuit receptacle?

My friends and I likes to play Trivial Pursuit without using the board. We play it like this: Throw a die to determine what color you get to answer. Ask a question, if the answer is correct you get ...
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 ...
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 $52$ ...
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 ...
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: ...
3
votes
2answers
41 views

A question on fundamentals of Probability and Random Variables

Suppose you own 6 shirts. Starting April 1st, you pick a shirt uniformly at random to wear each day. The choice of shirt is independent of one another. Assume that a shirt worn on a given day is ...
3
votes
1answer
485 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 ...
3
votes
1answer
113 views

Is there a name for this distribution? (generating until all numbers appear)

A computer program generates a number between $1$ and $n$ every second ( there is a $1/n$ probability for each number ). It continues until all $n$ possible numbers were generated. Let $X$ ...
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 ...

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