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's the probability of the max segment is equal to k?

There are $m$ integer points on a line of length $m-1$ (including the end point of the line). We randomly mark $n$ points of the $m$ points ($n\leq m$), dividing the line into several segments, so each segment have an integer length. What is the…
Fan Zhang
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Which versions of Chernoff bound are applied to Binomial distribution in these examples?

There are several versions of Chernoff bounds. I was wodering which versions are applied to computing the probabilities of a Binomial distribution in the following two examples, but couldn't. I have tried to find them out but not succeeded. From…
Tim
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how many times in average do I have to roll a dice to get a 1?

I've read that the answer to such a problem is the inverse probability. So here getting a one has probably 1/6, so the number of tries you would be expected to run in order to get a 1 is 6. I'm not sure I understand this.
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Simple yet confusing probability problem.

A bag contains x green candies and y red candies. A candy is selected at random from the bag and it's color is noted. It is then replaced into the bag with an additional ten candies of the same color. A second candy is then randomly chosen. Find the…
King KONG
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A pair of fair dice is rolled. What is the condition probability that one of the dice is a four given the sum is a seven

I believe that the probability of the sum is seven is (1/18), unless i'm wrong of course. I'm getting stuck getting the top value. Any help? Is the probability of one of the dice being four = 1/3? Then it would be (1/3)(1/18)/ (1/18)?
Killercamin
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Advantage of going first in a board game

I've been playing with my son a simple board game where you roll a regular 6 faced die and move as many positions as you roll. So nothing fancy, just pure luck game. Lately I've been trying to teach him that is not OK for him to always go first.…
Marius
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Probability of possessing a position among all.

Suppose with staggered entry, $5$ children have come to a teacher to learn alphabets. The teacher assigned them ID according to their arrival, that is, the teacher assigned ID $1$ to the child who came first to her, and then ID $2$ to the next…
ABC
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How to make unbiased coin from potentially biased coin, is my reasoning correct?

Problem: Let's say you have a coin that might be (you don't know how biased, or even whether biased in the first place) biased, and you want to come up with a way to simulate an unbiased flip. My reasoning (took me a few steps to get here but I'll…
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There is an $80\%$ chance of rain on each of the next $6$ days. What is the probability that it will rain on exactly $2$ of those days?

There is an $80\%$ chance of rain on each of the next six days. What is the probability that it will rain on exactly two of those days? Could you show the workings as well as showing in the equation format. I don't quite understand the equation…
probslater
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The probability that there will be 3 cloves with four leaves?

Suppose there is $1$% of cloves with four leaves. We pick $100$ cloves. Let $X$ denote the event a clove has four leaves. What's the probability of having 4 cloves? I am wondering which method should I use? 1st possibility: The first such clove has…
user401855
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Flipping Coins and Advantages

You and I decide to play a game where we take turns flipping a coin. The first player to flip 10 heads wins the game. Naturally, there is an argument about who should go first. Simulations of this game show that the player to flips first wins 2%…
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How can gender and class classification be dependent?

I got this question in my hw practice set In a class, there are 4 freshman boys, 6 freshman girls, and 6 sophomore boys. How many sophomore girls must be present if sex and class are to be independent when a student is selected at random? I solved…
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Rolling Dice Probability Question

Rolling a fair dice $7$ times, what is the probability that the total sum is divisible by $3$, and no odd value was rolled? I know that there are $3^6$ possible ways for the first $6$ dice to give only even values, but how many of them are divisible…
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Is this a trick question? Balls into urns probability

There are two urns. Urn 1 contains 3 white and 2 red ball, urn 2 one white and two red. First, a ball from urn 1 is randomly chosen and placed into urn 2. Finally, a ball from urn 2 is picked. This ball be red: What is the probability that the ball…
MugB
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Probability - find the number of balls in a box

There are $20\%$ less white than black balls in a box. Two balls are randomly chosen. If the probability that at least one chosen ball is white is $12/17$, how many black balls are in a box? If $w$ is the number of white balls, and $b$ is the number…
user300045
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