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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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unbiased estimator for geometric distribution

Let $X_1,\ldots,X_n$ to be sample distributed geometric with parameter $p$. Find MLE. Is it unbiased? The distribution for each is $p(1-p)^{x_i-1}$ so the function is $$L(p)=\displaystyle\prod_{i=1}^np(1-p)^{X_i-1}.$$ After taking lns on both…
user65985
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Probability of two intersecting straight paths

Two people, A and B, starts from two different points and move in a perfectly straight line in an infinite plane. When they move they leave a visible trace after them. Question: What is the probability that their path (of traces) will intersect at…
Prim3numbah
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Probability of number of equally spaced numbers

If you have a uniform sample of size $\ell$ of integers taken from $[1,\dots,n]$ which is then sorted, how do you calculate the probability that there exists an equally spaced subsequence of length $k$ (or at least $k$)? As an example, if the…
marshall
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Expected number of self loops.

You have 100 string in a bag and you randomly pull out one end of a string. You randomly pull out another end and tie them together. You do this until you have no more ends. The expected number of loops is $\sum_{i=1}^{n} \frac{1}{2n-1}$. What is…
narcissa
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Probability of Twisting a Phone Cord During a Call

I invented this problem and am unable to solve it. It is not a homework problem. I make a phone call on a standard handset (with a coiled cord). I start with the phone on my right ear. With probability p I talk long enough that I transfer the phone…
mckelvey
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Symmetric random walk on a regular hexagon

I wonder if there is any trick in this problem. The following graph is a regular hexagon with its center $C$ and one of the vertices $A$. There are $6$ vertices and a center on the graph, and now assume we perform the symmetric random walk on it.…
Tianjian Che
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Easy question on probability

I know this is a trivial question but I want to make sure I'm not missing anything: We have a biased 6-sided die, which brings any of the 6 numbers with equal probability in the first roll, but in the second and all subsequent rolls, brings the…
Samuel
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In a random graph of $n$ vertices, what is the expected value of the number of simple paths?

I am very new to discrete probabilty and was asked this question: In a random graph $G$ on $n$ vertices (any edge can be in the graph with probabilty of $\frac{1}{2}$,) what is the expected value of the number of paths between a vertex $v$ and a…
TheNotMe
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Boggle letter probability

How to distribute English alphabet letters among Boggle game dice? How to make rolling for example letter "A" more often than others? How to choose how many copies of each letter to make, and how many copies of them to put on one dice? Can you…
myself
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Explain to a 15 y.o. Byron Schmuland's answer that uses Summation and Product notations to solve the Crazy Lady Airplane Seat probability problem?

Byron Schmuland's answer1 is too abstruse for a 15 y.o. student who needs details! Please see my enumerated questions below. Let's find the chance that any customer ends up in the wrong seat. For $2\leq k\leq n$, customer $k$ will get bumped when…
user53259
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Probability that a given Poisson variable samples greater than its mean $\lambda$, provided $\lambda > D$

Given a random variable $X \sim \text{Poisson}(\lambda)$ such that $\lambda > D$, with $\lambda, D \in \mathbb{N}$, what is the probability that a sample obtained from $X$ is greater than $\lambda$? In other words, what is the value of $\mathbb{P}(X…
Arthur Araruna
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I throw a coin 10 times, and I get all heads, what is strange here?

I take a coin and with the assumption that it is a fair coin. I throw it 10 times and I get a sequence of 10 consecutive heads. I feel something is unusual and strange, may be the coin is not fair. But the outcome I got is as likely as any other…
Saeed Zargar
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Conditional probability

Given the events $A, B$ the conditional probability of $A$ supposing that $B$ happened is: $$P(A | B)=\frac{P(A\cap B )}{P(B)}$$ Can we write that for the Events $A,B,C$, the following is true? $$P(A | B\cap C)=\frac{P(A\cap B\cap C )}{P(B\cap…
user6163
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Probability question is bugging me

I recently saw a question somewhere where I got confused between what exactly I should do about it. Q. Imagine person A speaks truth 9 out of 10 times and another person B speaks truth 8 out of 10 times. A random card is picked from Jack, Queen and…
Vaibhav D S
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probability of getting a double six ($2$ dice) rolling them $24$ times

This is what I got. $\dfrac{1}{6} \cdot \dfrac{1}{6} = 2.78\% \cdot 24 = 66.72\%$ I believe that since it is a six sided dice, since you roll both of them simultaneously it would be $\dfrac{1}{6} \cdot \dfrac{1}{6}$. So since they are rolling them…
Ghozt
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