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 .

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Expected number of operations on a vector until one of the coordinates becomes zero.

Let's say we have a vector $v = (x_1, ..., x_n) \in \mathbb{N}^n$ where $x_1 = x_2 = ... = x_n$. Next we choose an ordered pair of coordinates at random $(i, j)$ where $i, j \in \{1, ..., n\}$ and $i \neq j$. Finally we substitute the vector $v$…
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$m$ balls $n$ boxes probability problem

I encountered this problem in my probability class, and we weren't able to solve it, so I would like to know the answer. If you have $m$ balls and $n$ boxes, with $n < m$, and you insert the balls into the boxes randomly, what is the probability…
alejopelaez
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Consistency and asymptotically unbiasedness?

Does consistency imply asymptotically unbiasedness? I know the statement doesn't work in the other direction. My guess is it does, although it obviously does not imply unbiasedness. I think it wouldn't be too hard if one digs into measure theory…
Vokram
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Average number of tosses to WIN the gambler's ruin game.

In the "gambler's ruin" game, you start with 'n' dollars. You keep betting 1 dollar (on heads), on coin tosses. The coin is biased to come out heads with probability = p. A game ends when you have gotten N dollars, N>n, (you won the game) or you…
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How likely is it for a randomly picked number to be larger than all previously chosen numbers?

Suppose we pick a uniformly distributed number on the range [a,b]. Then we continue to pick more numbers on the same range. Let n(t) be the number of times we have found a number bigger than any previously found, after sampling t total numbers. The…
user1535823
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Probability of winning in a die rolling game with six players

There are 6 players numbered 1 to 6, 1 Player, Player 2, ..., Player 6. Player 1 rolls a die , if he gets a 1 wins and the game ends, otherwise the die passes to the player whose number matches the number that presents the die and the player makes a…
Lisbeth
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The minimum of two independent geometric random variables

here's a question I got for homework (sorry if my translation is a bit unclear): Let $X\sim‬G(p_1)$, $Y\sim ‬G(p_2)$, $X$ and $Y$ are independent. Prove that the minimum is also geometric, meaning: $\min(X,Y)\sim G(1-(1-p_1)(1-p_2))$. Instructions:…
yotamoo
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The probability that x birthdays lie within n days of each other

This is a question that has bugged me for quite some time: what is the chance that x people happen to have their birthdays within n days of each other? A bit more specific, since this is how a colleague one phrased it: what is the probability that 5…
user88701
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Probability about three independent exponential random variables

Suppose we have three independent exponential random variables $A$, $B$ and $C$ with respective parameters $1$, $2$ and $3$. Calculate $P(A
geraldgreen
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Conditional and Total Variance

Why does $ \text{Var}(Y) = E(\text{Var}(Y|X))+ \text{Var}(E(Y|X))$? What is the intuitive explanation for this? In laymen's terms it seems to say that the variance of $Y$ equals the expected value of the conditional variance plus the variance of the…
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$1/2$ or $1$? probability that all bacteria will die

Suppose there is a bacterium in a bottle, it has $\frac{1}{3}$ chance to die and it has $\frac{2}{3}$ chance to split into 2 individuals, and the new individuals will follow this rule and so on. So here is the question, what is the probability that…
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Probability about a coin games

Independent flips of a biased coin that lands on heads with probability is 0.7 are made. Each of two players, A and B has chosen one out of the eight triplets HHH, HHT, HTH, HTT, THH, THT, TTH and TTT, and the player whose triplet occurs first wins.…
davaid
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p chance of winning tennis point -> what f(p) chance of winning game?

In Wii Tennis, I have fixed $\,\,p\,\,$ chance of winning a given point. What is my chance $f(p)$ of winning the entire game? If $p=0.5, f(p)=0.5$ by symmetry, but I believe $f(0.51) > 0.51 $ EDIT: to clarify, the rules of Wii Tennis are the same…
user2469
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How long does it take for a given number of Minecraft sugar cane plants to grow to full size?

In Minecraft, the growth of sugar cane plants is governed by random events. On each game tick (1/20th of a second), each sugar cane plant has a certain probability of advancing to the next stage of growth. The random event must occur 30 times for…
PhiNotPi
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You have 3 cakes. Everytime you eat one, there's 17% chance the number of cakes is reset to 3. Find average number of cakes eaten?

I did a Python simulation and the answer is 4.40. But I think there should be a theoretical approach for this problem. I remember having seen variations of it mutiple times but don't know the technical terms for it. If anyone is interested, here's…
HuN
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