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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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The probability of forming Mississippi by choosing random letters from Mississippi

I'm having difficulty with the following problem: You choose a letter at random from the word Mississippi eleven times without replacement. What is the probability that you can form the word Mississippi with the eleven chosen letters? Hint: it…
Sasaki
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expected length of broken stick

You break a stick of unit length in two. You then subsequently break the biggest of the resulting two sides in two, thus obtaining three pieces. What is the expected length of the smallest of the three? (Each breaking of a stick is assumed to be at…
alexandreC
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Please prove that the Probability Mass Function (in Binomial Distribution) is less than 1.

I have finished elementary probability and I know the sum of all probabilites in a data set is 1.But while reading Binomial Distribution,I encountered the formula for the Probability mass distribution : $$f(k ; n, p)=\operatorname{Pr}(K=k)= {n…
Ivy Mike
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Expected value of sums

Suppose we draw cards out of a deck without replacement. How many cards do we expect to draw out before we get an ace?
Alkha
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Why does P(HH) differ from P(TH)?

Suppose I keep tossing a fair coin until I get two consecutive heads or a tail and then immediately a head following it. Why are these two patterns not equally probable? I thought they were since the coin is fair... Should I model this problem using…
David Faux
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Three white and one red ball probability

Three boys play a game as follows. They put three white balls and a red ball in a box. Andy, Bruce, and Charles, in this order, each choose a ball at random from the box, without replacement. Whoever gets the red ball wins. If none of the three…
Dhruv Raghunath
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What is the probability of an independent event occurring after repeated attempts?

Let's suppose that I have an event whose probability of occurring is $\frac{44}{1000}$. Let's also assume that I can make multiple independent attempts at observing the event. I want to know what the compounded probability is that the event would…
Stephen
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Linearity of expectations - Why does it hold intuitively even when the r.v.s are correlated?

An experiment - say rolling a die, is performed a large number of times, $n$. Let $X$ and $Y$ be two random variables that summarize this experiment. Intuitively(by the law of large numbers), if I observe the values of $X$, over a large number of…
Quasar
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Probability that the difference of the max and min of three random numbers between 0 and 2 is less than 1/4?

Three numbers are chosen at random between 0 and 2. What is the probability that the difference between the largest number and the least number is less than 1/4? This is a problem from JHMT Calculus 2011. I'm trying to see if there are any better…
user381493
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Expected number of Pareto-optimal points

Suppose $S$ is a set of $n$ points in a plane. A point is called maximal (or Pareto-optimal) if no other point in $S$ is both above and to the right of that point. If each point in $S$ is chosen independently and uniformly at random from the unit…
CaptainObvious
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Probability of selecting two numbers with a sum of squares divisible by 10

Two natural numbers $x$ and $y$ are chosen at random. Find the probability that $x^2 + y^2$ is divisible by 10. I could not understand how select two numbers from any natural number (infinite).
a25bedc5-3d09-41b8-82fb-ea6c353d75ae
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Flies in a cube

Two flies sit in the corners $(1, 1, 1)$ and $(n, n, n)$ of a discrete cube $M^3$, where $M=\{1,\ldots, n\}$. After every unit of time both flies decide randomly and independently of each other whether or not to fly to some neighbouring point; here…
Damian Reding
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Probability in flipping a coin

Independent flips of a coin that lands on heads with probability p are made. What is the probability that the pattern T, H, H, H occurs before the pattern H, H, H, H? Hint: How can the pattern H, H, H, H occur first? my approach is…
user133466
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Conditional probability is undefined even though it seems defined intuitively

We know that conditional probability $P(A | B)$ is undefined when $P(B) = 0$. But this doesn't seem to be true to me always. Consider the probability of chosing a real number between $r$ such that $0 \leq r \lt 1$ where any real number in $[0, 1)$…
Lone Learner
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Drawing two cards from a deck of 16 (4 ranks and 4 suits)

I'm reviewing for an exam and have come across a problem marked incorrect on my homework. The problem reads, There are 16 cards in a deck. The cards have 4 ranks (Jack, Queen, King, and Ace) and 4 suits (Clubs, Diamonds, Hearts, and Spades). You…
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