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 ...
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 ...
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 ...
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, ...
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 ...
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 ...
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 ...
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 ...
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 $52$ ...
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 ...
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: ...
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 ...
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 ...
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 $X$ ...