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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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What is the name of this formula derived from the Poisson distribution?

I am learning about the Poisson distribution in this document and its link reference. This is the key formula to compute the Poisson distribution: $$ f(k; \lambda)=\frac{\lambda^k e^{-\lambda}}{k!} $$ I saw another related formula…
JJJohn
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If you are wrong twice you have more chance of being right

Imagine you are having a test in high school, the teacher says "you have two minutes until I take your test". You are doing the last question and you are clearly wrong, you have no time to redo the question. what should you do? my theory says…
yuvi1
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Probability no one needs to wait for changes when buying tickets .

There are $2 \cdot n$ people in the queue to the theater office; n people on only banknotes worth $20$ zlotys, and the remaining n people only have banknotes worth $10$ zlotys . At the beginning of the sale at the box office there is no money. Each…
Eac97
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The draw for the fifth round of the FA Cup

The draw for the fifth round of the FA Cup is about to be made. There are 16 teams, leading to eight matches. Your task is to pair the teams off, in an attempt to guess as many as possible of the actual matches in the real Cup draw. You are not…
osita unegbe
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Probability of matching 5 cards from a deck of 40

Suppose we have a deck of 40 cards which has, 5 Aces, 6 Kings, 9 Queens, 20 Jacks. A game is played where a contestant will continuously draw cards until they have 5 matching cards (not necessarily in order). The cards are drawn without…
DH.
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Maximum and Minimum Variance

Let $p_i =P(X=i)$ and suppose that $p_1+p_2+p_3=1$. If $E[X]=2$, what values of $p_1,p_2,p_3$ (a) maximize and (b) minimize $Var(X)$? So far I have $Var(X)=E[(X-E[X])^2]=E[(X-2)^2…
photon
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How do we arrive at the conclusion that P(Head) =0.5 for a fair coin?

In Feynman's 'Lectures on Physics', I read a chapter on probability which tells that P(Head) for a fair coin 'approaches' 0.5 as no. of trials that we take goes to infinity (well, I tossed the coin 50 times & got heads 17 times, instead of 25 :-)…
amitlan
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Biased coin question

You have a biased coin, where the probability of flipping a heads is $70%$. You flip once, and the coin comes up tails. What is the expected number of flips from that point (so counting that as flip $\#0$) until the number of heads flipped in total…
rohan bagri
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If $P(A \cup B \cup C) = 1$, $P(B) = 2P(A) $, $P(C) = 3P(A) $, $P(A \cap B) = P(A \cap C) = P(B \cap C) $, then $P(A) \le \frac14$

We have ($P$ is probability): $P(A \cup B \cup C) = 1$ ; $P(B) = 2P(A) $ ; $P(C) = 3P(A) $ and $P(A \cap B) = P(A \cap C) = P(B \cap C) $. Prove that $P(A) \le \frac{1}{4} $. Well, I tried with the fact that $ 1 = P(A \cup B \cup C) = 6P(A) - 3P(A…
Anne
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What does the value of a PDF mean?

I understand that the integral of a PDF provides tangible value --i.e., the integral of a PDF allows one to see the probability of a value or less than that value, under a particular distribution, occurring. But, what does the value of just the…
Lea
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Prove $E[X/Y]\ge1$ for X,Y iid positive random variables.

Prove $E[X/Y]\ge1$ for X,Y iid positive random variables. My attempt: Let $Z=X/Y$ $Z\in(0,\infty)$. $$E[Z]=\int_0^\infty P(Z\gt z)dz=\int_0^\infty P(Y\lt{1\over z}X)dz$$ $$=\int_0^\infty\int_0^\infty\int_0^{{1\over…
clement
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How to calculate a (possible) chance from a zero-incidence sample?

This is probably a very simple problem, but I want to make sure I have a correct understanding. I have a sample of $500$ events, in which a complication $C$ didn't occur. How do I calculate a reasonably correct chance for $C$? Would that be just…
Joris
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probabilty problem how to solve

Six cards are drawn with replacement form on ordinary deck. What is the probabilty that each of four suits will be represented at least once among the six cards?
Devendra
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Why don't we always consider complete measure spaces?

Let $(\Omega ,\mathcal F,\mathbb P)$ a probability space and let $X=(X_t)$ and $Y=(Y_t)$ two stochastic processes. I know for example that $X$ and $Y$ are indistinguishable if there is a set $N$ of measure $0$ s.t. for all $\omega \notin N$ we have…
user621345
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What is the probability of three consecutive results X and two results Y in an event?

I have N number of days where three different events X,Y,Z can occur in each day. A is a set of possible occurrences of length N. I want to calculate the number of ways where: Y does NOT happen twice or more in these number of days N X does NOT…
user3026388
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