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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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Birthday Problem without using complement

I have a solution to the birthday problem without using complements that is arriving at the wrong answer. I'd like to understand what I am doing wrong. I am not looking for alternate solutions to the problem. Problem Assuming there are only 365 days…
Nick Desai
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Probability of getting at least one job offer based on interview odds

I have recently interviewed for a number of jobs, and am wondering what the odds are of getting accepted for one based on the odds of each interview and the total number of interviews. I had $7$ interviews which had a $1$ in $10$ chance of…
Yi Calvert
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Choosing the best or second best secretary

We have a hall with $N$ secretaries. We choose randomly one secretary at a time and interview them. After the interview either we hire the secretary (and all others go home) or move to the next one (we can't go back and hire them later). The…
Adddison
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Conditional probabilities with impossible outcomes

Suppose we want to predict the outcome of a race between three runners $A$, $B$, $C$. We know the prior probabilities for head-to-head runs: $p_{A>B}$, $p_{A>C}$, $p_{B>C}$, where $A>B$ means that A finishes before B. How do we get the probability…
Darina
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Expectation of $ X(X - 1) \ldots (X - k + 1) $, where $ X $ has a Poisson distribution.

I am trying to calculate $$ \text{E}[X(X - 1) \ldots (X - k + 1)], $$ where $ \text{E} $ denotes the expectation operator and $ k \in \mathbb{N} $ is fixed. I think I have to use the fact that the expectation of a sum of random variables is the sum…
user1324258
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How do I solve a probability problem involving permutations and having two steps?

The problem: A man spends 7 nights in a city. He has a list of the 8 best Italian restaurants and the 9 best Chinese restaurants. How many ways can he eat 7 meals at these restaurants, assuming a different restaurant each night and he wishes to…
Thomas Grode
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Order in a Biased Coin

Situation: Consider the classic coin tossing experiment. We want to explore if the coin is biased. Coin 1: Coin is tossed $50$ times. We get $20$T and then $30$H, in that sequence Coin 2: Coin is tossed $50$ times. We get $4$T $6$H, $4$T $6$H,…
Penrose
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When defining independence of random variables,do they need to be on the same probability space?

Random variable X and Y with cumulative distribution functions $ F_X(x)$ and $F_Y(y)$,are independent iff the combined random variable $(X, Y)$ has a joint cumulative distribution function $$F_{X,Y}(x,y) = F_X(x) F_Y(y)$$ In the above…
Spaceship222
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Probabilty of having exactly one sibling

I'm stuck on the following probability problem: parents keep having children until they have one girl, at which point they stop; and babies are girls with probability 0.49. If we select a child uniformly at random (from the entire population of…
Ana
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What is the probability that white balls will be in the same box?

I have trouble computing a probability, I wish someone can help me with this. This is not a homework or anything like that. So there are $71$ balls, and two of them are white, the rest are black. The balls are randomly distributed between $14$…
Sebastian Smith
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We lost two cards from a deck of $52$ cards. If we extract a card of this deck, what is the probability we get a diamond?

We lost two cards from a deck of $52$ cards. If we extract a card of this deck, what is the probability we get a diamond? I'm confused here. Suppose we lost two diamonds, then $$P(\text{we get a diamond})=\frac{11}{50}$$ but, if we lost two cards of…
rcoder
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Expected length of arc in a randomly divided circle

Choose, at random, three points on the unit circle. Interpret them as cuts that divide the circle into three arcs. Compute the expected length of the arc that contains the point (1, 0). Generalise for N points.
alexandreC
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A question about probability (conflicting solutions)

There is a square of side $n$ units. Join the diagonals. Now the square is divided into 4 regions of equal area. Each of them is coloured differently. Given 2 points that can lie within any of the four regions, what is the probability that two…
user406287
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Expected Value of random variable raised to another random variable

If $X$ and $Y$ are continuous random variables uniformly distributed over $[0,1]$, find $E(X^Y)$. My first thought was that $E(X^Y) = E(X)^{E(Y)}$, but through simulation I found that this was not the case. I then tried using a double integral from…
Lun Wei
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Probability of success and failure

I've an interesting question on my hand which I've approach several others but all of them gives me different insights to this probability question. Here it is, The incidence of a suspicious transaction in a bank is 1 in 149. They are able to…
Astral Zhang
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