Questions tagged [probability]

For questions about probability. independence, total probability and conditional probability. For questions about the theoretical footing of probability use [tag:probability-theory]. For questions about specific probability distributions, use [tag:probability-distributions].

The probability that an event occurs is a number in the interval $[0, 1]$, which represents how likely the event is to happen. $0$ indicates it will never happen, $1$ indicates it will always happen.

For example, throwing two dice gives a total of $6$ five times out of thirty-six. We write $$P(X=6)=\frac{5}{36}$$.

Use this tag for basic questions about probability, independence, total probability and conditional probability.

For questions about the theory of probability, use instead. For questions about specific probability distributions, use .

105859 questions
8
votes
2 answers

Given enough time, what are the chances I can come out ahead in a coin toss contest?

Assuming I can play forever, what are my chances of coming out ahead in a coin flipping series? Let's say I want "heads"...then if I flip once, and get heads, then I win, because I've reached a point where I have more heads than tails (1-0). If it…
Beska
  • 218
8
votes
1 answer

Find distribution when given Moment generating function

I am trying to find the distribution that corresponds to this moment-generating function. $$ M(t) =\frac{1}{3e^{-t}-2} , \quad t < \ln \frac 3 2 $$ I can not even consider where to start. Any push in the right direction would be appreciated!…
8
votes
2 answers

Probability question on dice

A fair die is rolled. Each time the value is noted and a running sum is maintained. What is the expected number of runs needed so that the sum is even?
rohit
  • 387
8
votes
2 answers

Why can't all subsets of sample space be considered as events?

My textbook is Probability and random processes by Grimmett & Stirzaker and the first chapter does not explain this," for reasons beyond the scope of the book". The authors introduce the reader to sample spaces and to events and then go on to say…
Anupam Kumar
  • 83
  • 1
  • 3
8
votes
1 answer

prove the way to generate geometrically distributed random numbers

The way to generate geometrically distributed random numbers is the following $$\lfloor{\ln(u)/\ln(1-p)}\rfloor$$ where $u$ is uniformly distributed in $[0,1]$ and $p$ is the parameter in the geometric distribution. But can anybody help provide a…
Qiang Li
  • 4,097
8
votes
7 answers

Probability I have another pack of sweetener

I drove my motorcycle to a fast food restaurant the other day. As I was waiting for my lunch, I noticed they still had their coffee condiments out. Not having any at home, I decided I'd grab a small handful and toss them into my motorcycle bag for…
8
votes
1 answer

Asking for an "intuitive" explanation of a probability problem

The problem is as follows: We pick a real number p in $(0,1)$ randomly and uniformly, then construct a coin such that when tossed, $P(H) =p$ and $P(T) = 1- p$. Now fix a positive integer $n$, if we were to toss the coin $n$ times (independently),…
StAKmod
  • 1,338
8
votes
4 answers

Probability - two balls in the box: one we don't know its color and the other is red. What's the probability it's white?

Bob has a black box (you can't see what's inside the box). A long time ago Bob put one ball into the box but he doesn't remember what color the ball was. With equal probability it can be a white ball or a red ball. A. Bob takes a red ball and puts…
8
votes
1 answer

pairwise disjoint events example

Can someone please give me an example of a pairwise disjoint event? Let $S = \{1,2,3,4,5,6,7,8,9\}.$ Will pairwise disjoint events be: $\{1\},\{2\},\{3,4\},\{5,6,7,8,9\}$? In order to be pairwise disjoint event does it just mean that for all $A_i$…
8
votes
3 answers

Coin tosses with unknown success probability

Suppose I have a coin with unknown probability of success (let say Heads) $p$ which is uniformly distributed on $[0, 1]$. I toss a coin $N$ times. What is the probability that I have got $n \leq N$ Heads? Ok. I've calculated (using Wolfram) that…
dEmigOd
  • 3,308
8
votes
6 answers

Probability of $n$ times a $\frac1n$ event

I never studied probability at school and this problem has been bothering me for a long time: Let's say I have a perfectly fair die. If I roll it, the odds of it landing on $6$ are $\frac{1}{6}$. If I roll two dice, the odds of at least one of them…
eje211
  • 235
8
votes
4 answers

Odds of being correct X times in a row

Is there a simple way to know what the chances are of being correct for a given number of opportunities? To keep this simple: I am either right or wrong with a 50/50 chance. What are the odds that I'll be correct 7 times in a row or 20 or simply X…
8
votes
3 answers

When can i get away with approximating the expected value of a ratio as the ratio of expected values

I'm actually an engineering student so I'm not too good with probability and was hoping someone may be able to help with the following: So I have a ratio of discrete random variables. I want to be able to know when I can get away with approximating…
8
votes
1 answer

Replacement only when 'prize' is found

There are $a$ balls in a jar. One is gold, the rest are black. Balls are taken from the jar. If a black ball is taken, it is not replaced. If a gold ball is taken, all balls are replaced. I am interested in finding a closed form solution for the…
Shuri2060
  • 4,353
8
votes
2 answers

Expected length of a sequence that contains all words of a given length.

Fix some alphabet $\Sigma$ and a positive integer $n$. What is the expected number of random letters drawn from $\Sigma$ until all length-$n$ words are present? For example, let $\Sigma = \{0,1\}.$ Then the string "10" contains all possible…
Fixee
  • 11,565