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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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A Probability question: last ball in the bag

Players are pulled up to pick a ball out of a hat containing $14$ red and $1$ blue. If the odds of drawing the blue ball are $1/15$ what are the odds of every person not drawing the blue ball and leaving it for the last person to draw? Initially I…
Kenny Hammerlund
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conditional probability on two variables

How can you express p(x1|x2,x3) in terms of p(x2|x1,x3) and p(x1|x3) and p(x2|x3) with the help of the chain rule…
james
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Why does a filtration represent information over time?

The book I am reading says that Ft contains all events whose occurrence or not is fixed by time t. Why is this the case? Let say A is an event that has not been fixed yet, B is an event that has been fixed. Then A union B has to be in Ft, but A…
user1559897
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Is this a combinatorial identity: $ \sum_{k=1}^{n+1}\binom{n+1}{k} \sum_{i=0}^{k-1}\binom{n}{i} = 2^{2n} $?

$$ \sum_{k=1}^{n+1}\left(\binom{n+1}{k} \sum_{i=0}^{k-1}\binom{n}{i}\right) = 2^{2n} $$ This is my first question, please feel free to correct/guide me. While solving a probability problem from a text book l reduced the problem to the above LHS. I…
Kartik Mahajan
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probability of a large sub-sequence within a huge sequence

You toss a fair coin one million times. What is the probability of getting at least one sequence of six heads followed by six tails?
alexandreC
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probability involving rerolling dice

The question go like the following. You roll one 6 sided dice one time. You get the same money as the number of dots face up. But if you roll a six, you get nothing and re-roll. If your re-roll gets a six again, you reroll again and again. What is…
Ricky Ng
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Probability of Occurence of HEART or EARTH

This is one of the questions I came across and I could only solve it partially. The question went A man is randomly typing on a keyboard. Then, what is the probability that the word HEART comes before EARTH? My attempts The first $4$ letters of…
Your IDE
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Expected value of $X$ given $X > 15$

If $X$ is a poisson random variable with $\lambda =\frac{1}{15}$, what is the expected value of $X$ given $X > 15$ ? I should know this but it's been a while since my intro to probability class.
Tatiana Frank
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Probability of the correct answer

I was learning for the test, when I spotted problem that I cannot deal with: We have an algorithm that gives correct answer with a probability $p>\frac{1}{2}$. For simplicity assume that the answer is an integer. To increase the probability of…
xan
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Overtaking Probability

On a uni-directional circular road where all vehicles travel in the same direction with varying speeds and overtaking is allowed on the entire road, what is the expected number of times (a) a particular vehicle will overtake others? (b) a…
user7896
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A deck of 40 cards, 4 suits from 1 to 10, 2 cards extracted, probability the sum is 9?

You have a deck of $40$ cards, $4$ suits from $1$ to $10$, pick randomly $2$ cards, no reimmission, what is the probability you get $9$ as a sum? How can I solve using the basic principle of counting? The favorable outcome are $(8+1)*4$, $(7+2)*4$,…
MarNo
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What are the odds of cracking a cellphone pattern-lock?

In case someone don't know what a pattern lock is, they are like this: I am curious on the probability of randomly cracking one of these 'passwords', given that the length of the grid is 3x3 and that we know the pattern length (e.g number of…
ajax333221
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If numbers of heads and tails are independent, then number of tosses $N \sim \mathrm{Poisson}$

A fair coin is tossed a random number $N$ of times, giving a total $X$ of heads and $Y=N-X$ tails. Show that if $X$ and $Y$ are independent and the generating function $G_N(s)$ of $N$ exists for $s$ in a neighbourhood of $s=1$, then $N$ is Poisson…
Václav Mordvinov
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Expectation of the product of two discrete random variables.

Let $X_i, X_j$ be two random variables that can each assume the values $\zeta_1, ..., \zeta_m$. Then my book claims $E(X_iX_j) = \sum_{k = 1}^m\sum_{l = 1}^m\zeta_k\zeta_lP(X_i = \zeta_k \textrm{ and } X_j = \zeta_l$). I don't get how they acquired…
user388557
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How is the Erlang pdf derived?

If each arrival is exponentially distributed, then the $k$th arrival time is Erlang distributed. The Erlang PDF is: $$ f_{Y_k}(y) = \lambda e^{-\lambda y} \frac{(\lambda y)^{k-1}}{(k-1)!} $$ How is this derived?
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