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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Recursive formula for the probability that the starting player wins [DBertsekas & JTsitsiklis P57, 1.21]

Two players take turns removing a ball from a jar that initially contains $w$ white and $b$ black balls. The first player to remove a white ball wins. Develop a recursive formula that allows the convenient computation of the probability that…
user53259
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What is the probability that you toss next time, heads turns up

A bag contains 5 coins. Four of them are fair and one has heads on both sides. You randomly pulled one coin from the bag and tossed it 5 times, heads turned up all five times. What is the probability that you toss next time, heads turns up. (All…
rohit
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Rank of second ace after first ace is drawn

I have a probability problem with cards and the expected value of a card rank. I have a deck of 52 cards. I draw cards without replacement. While drawing cards from the deck, a first ace is drawn at rank $k$ (that is the $k^{th}$ card drawn is an…
alex_C
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Probability problem : A lot of 100 bulbs from a manufacturing process is known to contain 10 defective and 90 non ...

Problem : A lot of 100 bulbs from a manufacturing process is known to contain 10 defective and 90 non defective bulbs. If 8 bulbs are selected at random, what is the probability that there will be at least one defective bulb. Method I :…
Sachin
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Probability of insurance claims

Under an insurance policy, a maximum of five claims may be filed per year by a policy holder. Let $p_n$ be the probability that a policy holder files $n$ claims during a given year, where $n = 0, 1, 2, 3, 4, 5.$ An actuary makes the following…
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Does "gerrymandering" matter?

In the United States, it is often a raw point discussing the issue of redistricting, or so unfavorably called, "Gerrymandering." Background: In the United States House of Representatives, each State is allotted a number of representatives based on…
Mr. AM
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marble probabilities

A bucket has 3 marbles numbered 1, 2, and 3. Choose one and put it back along with another marble with the same number. Now choose a second and put it back along with a marble with the sum of your first two picks. Choose one more marble. Find P(the…
No Name
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The probability that 25 people do not have the same birthday

I figure that it would be something like this $$\frac{365}{365} \times \frac{364}{365} \times \cdots \times \frac{340}{365}$$ But that is a lot of fractions to enter into a calculator, even so I think this is the right answer but I was wondering if…
Algific
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Probability - exactly one of A and B occurs

$A$ and $B$ are events that are subsets of the sample space. $C$ is the event that exactly one of $A$ and $B$ occurs. 1) Write an expression for $C$ in terms of unions, intersections and complements involving the events $A$ and $B$ 2) Let $P$ be a…
Luke Edwards
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Compute the mean of $(1 + X)^{-1}$ where $X$ is Poisson$(\lambda)$

Question Let $X$ be Poisson with parameter $\lambda$. Compute the mean of $(1 + X)^{-1}$. (Introduction to Probability Theory, Hoel, pp. 104) Answer Key The answer key shows that the mean is $\lambda^{-1}(1 - e^{-\lambda})$ My Solution $$E(1 +…
NasuSama
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probability of at least a fraction of bins contain a fixed number of balls

Consider the process of throwing m balls into n bins. Each ball is thrown into a uniformly random bin, independent of other balls. What is the probability that at least a constant fraction of bins get a fixed number of balls.
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Does the likelihood of an event increase with the number of times it does not occur?

I would seem logical that the more times an event does not happen, the more likely it is to happen, for example: If a coin is flipped and it lands on tails 10 times in a row it would seam more likely that the next flip will result in heads. The…
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Probability of Drawing a Card from a Deck

I like to play Magic: The Gathering, and I'm interested in calculating the probability of certain things in the game. After drawing 7 cards from a 60 card deck, what is the probability that draw will contain at least one of x, where x is a card…
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Compute probability of winning a game with coins, without using series

I found the following question in a book with an answer. Question: You have two kinds of coins. The number of coin $A$ you have is $n$. The number of coin $B$ you have is $n+1$. When you throw all coins at the same time, calculate the probability…
mathlove
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Probability that n people will get one right and one left shoes from n pairs of shoes.

Suppose we have a closet with n pairs of shoes. n people will randomly pick 2 shoes from the closet. What is the probability that all of them will have 1 right shoe and 1 left shoe? My approach to this question was like this: We have $C(2n,2)\times…