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 .

105859 questions
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Expected value of sum of dice roll (one 6 side and one 10 side dice)

You have 2 dice, one 6-sided dice and one 10-sided dice. You get the dollar amount of the sum of the 2 dice. If unsatisfied with the current roll, you may pay 1 dollar to re-roll. How much would you pay to play the game, or what is the expected…
QRIUS2KNW
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Probability of Trees Being Planted Correctly

OK, so here is a real-world problem that I am actually facing, right now. I ordered ten almond trees from a nursery: 6 Texas Mission (TM), and 4 Hall's Hardy (HH) which are pollinators for each other. I have two plots that the trees are to go in,…
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Probability of even number of dice result

Suppose we roll a dice (with 6 sides) 21 times. What are the odds of getting either 1 or 2 an even amount of times? I tried to calculate it by representing the number of times we get 1 or two as a binomial variable $B(n=21, p=\frac{1}{3})$, And…
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Optimal Strategies for Coin-Flipping Games

My nephew thought of the following problem over the holidays: I have 100 coins, half these coins are currently face up heads, the other half are currently face up tails. Currently, my score is 0. Each coin has a 0.5 probability of landing on heads…
SiuMai2k22
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Borel-Cantelli lemma variation

Consider $(X_i)$ independent events such that $\sum_{i = 1}^\infty P(X_i) = \infty$ Let $S_n = \sum_{i = 1}^n \mathbb{1}_{X_i}$, then $\frac{S_n}{\mathbb{E}S_n} \to 1$ almost surely. Do you have any ideas how to prove this? I've been thinkint about…
Turtle5
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Expected number of trials until n-th success urn problem without replacement

I have a close relative of the urn problem, but with a slight twist. Given an urn containing $r$ red balls and $b$ blue balls, how many balls should I expect to pull out of the urn before I have pulled $d \leq b$ blue balls out of the urn? In the…
zelinka
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What is the probability that the sum of two random numbers is less than a given number?

Let us assume a pure random number generator generates a random number between the given range $[0,m]$ with equal probability. Given $m_1$, let it generate a random number($r_1$) in the range $[0,m_1]$. Given $m_2$, let it generate a random…
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Probability of red balls present in the urn

There are n total balls in the urn containing red and blue colors with unknown ratios. k red balls can be anywhere from 0 to n being equally likely and the remaining n-k will be blue balls. What is the probability of k red balls in the urn if the…
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Probability and independence

I am trying to solve a particular probability question. I have a fair 10-sides die, whose sides are labelled 1 through 10. I am trying to find the probability of rolling a multiple of 5 or an odd number. I find the probability as: P(multiple of…
Joebevo
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If I roll 2 dice and then add those 2 numbers together. What is the probability that the sum is $\le 5$ or that the sum is $\ge 11$

I want to solve this dice problem but I'm not sure if my solution is the most efficient way. If I roll one dice and then one more and then add those 2 numbers together. What is the probability that the sum is $\le 5$ or that the sum is $\ge 11$ ? I…
Bioelli
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Find the variance for the number of runs

A biased coin is tossed $n$ times and heads shows up with probability $p$ on each toss. Let us call a sequence of throws which result in the same outcomes a run, so that for example, the sequence HHTHTTH contains five runs. If $R$ is a r.v.…
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What is the probability that you stop at only the first stop light?

There are two traffic lights. Let $E$ be the event that you stop at the first light and $F$ be the event that you stop at the second light. Given: $P(E) = .6$ $P(F) = .4$ $P(E \text{ and } F) = .25$ What is the probability that you stop at only the…
user637978
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What is the probability that exactly 2 repairers are called out of 4 repairers?

A town contains 4 people who repair televisions. If 4 sets break down, what is the probability that exactly 2 of the repairers are called? I know that the solution is $$\frac{6 * (2^4-2)}{4^4}$$ But I don't understand why we do $-2$ the the…
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Mutually Exclusive question

If we have $P(a)=0.6, P(b)=0.7$, can we say they are not mutually exclusive? without any further infotmation? For example, is there a possible that $b$ depends on $c$, like this $p(b \mid c)$, right now we only have $P(b)=0.7$ and $P(a)=0.6$, can we…
Raymond
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Expected value for a random variable

I have 25000 numbers and I randomly pick one by ony until I get one that I've already picked. I want to know the expected number of picks that need to be made. The expected value in my opinion should be calculated as 1/25000*1 +…
Will
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