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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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Are these conditions sufficient to calculate this expectation?

We have \begin{aligned} E(Z_1) = A \\ \Pr \{ Z_2 = Z_1 + 1 \} = \frac 1 2 \\ \Pr \{ Z_2 = Z_1 - 1 \} = \frac 1 2 \end{aligned} Are these conditions enough to get $E(Z_2)$?
NonalcoholicBeer
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Probability problem ( shuffling cards )

Suppose we shuffle a deck of 10 cards, each bearing a distinct number from 1 to 10, to mix the cards thoroughly. We then remove three cards, one at a time, from the deck. What is the probability that we select the three cards in sorted (increasing)…
user2232305
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What are the exact odds of getting a perfect NCAA bracket?

With the NCAA March Madness Finals nearing, I thought it'd be appropriate to ask this. From everything that I've read and heard online, there seems to be varying opinions on the exact odds of getting a perfect NCAA bracket, especially from different…
yuritsuki
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Probability of dividing a deck of cards into 4 equal piles each containing an ace

After dividing a standard deck of cards into 4 equal sized piles, what's the probability that exactly one ace is in each pile? I've had a couple of ideas about how to set this problem up but nothing seems to come out correctly. For instance, I can…
anon
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Lottery probability

In the UK the lottery uses numbers $1$ to $49$ and a total of six numbers are picked. It has been said may times that there is as much chance of numbers $1, 2 ,3 ,4 ,5 ,6$ to be picked as any other random combination. My question is this: Let's say…
user2400
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On Chernoff bound

Suppose $X\sim \textrm{Binomal}(n,p)$, show that for $\epsilon\geq 1$ $$P\bigg\{{X/n \over p}\geq \epsilon\bigg\}\leq \exp\bigg[-np(\epsilon(\log \epsilon -1)+1)\bigg]$$ I suppose there is a way of using Chernoff Bound of some kind but I don't quite…
Roy Alan
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Conditional probability problem

An Internet search engine looks for a keyword in 9 databases, searching them in random order. Only 5 of these databases contain the given keyword. What is the probability that it will be found in at least 2 of the first 4 searched databases? What I…
Kelly
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Find the probability the same color was used twice in a chess game given the player did not lose

Here's the question and its solution: I don't see how the solution to the problem is to compute: $[1-P(W|L)]^2+[1-P(B|L)]^2$ i.e. I don't think the expression above reflects what the question is asking and I actually computed…
mauna
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To prove the independency of two random variables

Suppose two random variables $X_1$ and $X_2$ are of identical independent distribution, with the same PDF $f(x) = e^{-x}, \space x>0$. Now, we have $$Y_1=\min(X_1, X_2)$$ $$Y_2=\max(X_1, X_2)$$ $$Y_3=Y_2 - Y_1$$ The problem is to determine if…
John-Annual
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Probability of number of random answers being correct.

My teacher gave us a true-false test with 100 "questions." Only there were no questions. He had an answer key and was trying to prove that if we answered true and false questions randomly, the class average would be around 50%. I got 7 right out…
Laura
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Chance of adjacent lockers with the same combination

One weird thing that happened to me in high school was that the combination lock on my locker had the exact same combination as the locker next to it. It always struck me that the odds were crazy on this, but I never calculated it. The lock was a…
AdamFortuna
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Probability that a geyser erupts

Lets say you have a geyser that has a 2/3 probability of erupting in a 50 minute interval? What is the probability that it will erupt in a 20 minute interval? The way I tried to solve it that a 20 minute interval is 2/5 of a 50 minute…
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Conditional covariance.

Suppose we have two random variables, $X$ and $Y$, defined over nonnegative reals. Obviously, the following formula holds: $$\mathrm{Cov}(X,Y)=\mathbb{E}\left[XY\right]-\mathbb{E}\left[X\right]\mathbb{E}\left[Y\right].$$ However intuitional it may…
Johnny Westerling
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An alternative solution to a probability problem

The text states: There are 3 seniors and 15 juniors in Mrs. Gillis’s math class. Three students are chosen at random from the class. What is the probability that the group consists of a senior and two juniors? I answered this correctly by…
Nick
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simple random walks on undirected graphs

Consider a simple random walk on a undirected, connected graph. This is the random walk which, at every time step, moves to a random neighbor, with all neighbors being equally likely. Lets assume every node has a self-loop to avoid issues associated…
angela o.
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