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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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Expected value of the product of random integers summing to a constant value.

For $1 \le i \le n$, let $X_i$ be $n$ integer-valued random variables that sum to the constant $s$. None of the $X_i$ are zero and they can have identical values. I need to find the the expected value of the product of the random variables, i.e.…
keng5
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If A and C are independent, is P(A,C) = P(A)*P(C) always true?

Here is the original question. Of three possible events, event A is independent of the other two, and events B and C are mutually exclusive. The probabilities that the individual events A, B, and C will occur are 0.5, 0.3, and 0.2, respectively. …
xorxorxor
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Is the $P(\text{You Die})=1$?

So I was teaching my younger brother Probability and in order to give him some intuition, I told him that events that occur for certain have a probability of $1$. So events such as one dying will have a probability of $1$. Later, I was trying to…
Student
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When should I grab a bag of money?

100 small bags of coins are placed in a large cauldron. The 99 of these bags that contain pennies have the same size. The single small bag of quarters is twice the size of a single bag of pennies. The probability of grabbing each bag is proportional…
David Faux
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Why probability of unordered samples is not equally likely?

Consider a survey where a sample of size k is collected by choosing people from a population of size n one at a time, with replacement and with equal probabilities. Then the n^k ordered samples are equally likely, making the naive definition…
Majeed Siddiqui
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Explanation of the formula for combinations without repetition, probability

The formula for combinations without the repetitions is as follows: $$ \frac{n!}{r!(n-r)!}$$ This is achieved by doing $$\frac{n!}{(n-r)!}*\frac{1}{r!}$$ What I don't understand where $\frac{1}{r!}$ comes from. I know that the first part is what you…
Segmentation fault
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Finding out probability that the last digit of a product is 5

If $n$ positive integers taken at random are multiplied together, show that the probability that the last digit of their product is 5 is $$\frac{5^n-4^n}{{10}^n}$$ My attempt: Let $n$ positive integers be $x_1,x_2, \cdots ,x_n$. Let $a=x_1 \cdot…
Navin
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An experiment is repeated, and the first success occurs on the 8th attempt. What is the success probability for which this is most likely to happen?

An experiment is repeated, and the first success occurs on the 8th attempt. What is the success probability for which this is most likely to happen? So we want to find $p$ between $0$ and $1$ which maximizes $(1-p)^{7}p$. To do this we could take…
b_pcakes
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Probability question with interarrival times

(Why did the chicken cross the road?) A chicken wants to cross a single-lane road where the cars arrive according to a Poisson process with rate $\lambda$. She needs at least $k$ minutes to cross the road safely, so she will have to wait until she…
user39325
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What's the probability that one goldfish eats more than 2 pellets?

I scatter 10 pellets among the 7 goldfish in my tank. Assuming each goldfish has equal probability of obtaining any pellet, what is the probability that at least one goldfish eats over 2 pellets? I tried to solve this problem by asking the reverse…
David Faux
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Is $\mathbb{E}[Y|X]$ a random variable?

If X and Y are random variables, is $$\mathbb E[Y|X]$$ a random variable also? Intuitively it seems to be the case, but I can't explain why.
Andrew Kinsella
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Probability on accident

There were four accidents in a town during a seven-day period. Would you be surprised if all four occurred on the same day? If each of the four occurred on a different day? I couldn't figure out how to solve this problem. It looks like that it is…
sv_jan5
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Inequality of probablity.

Let $(S,F,P)$ be probability space and $X :S \rightarrow \mathbb{R}$ be random variable with mean 0 and variance 1. Let $c \geq 0$. I want to show that $P(X \geq c) \leq \frac{1}{1+c^2}.$ I already know Chebychev inequality $P(X\geq) \leq 1/c^2$…
Seongqjini
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Deck of Cards Probability: Two lost cards, one drawn—what is its suit?

I'm having trouble with a probability problem and would love for an explanation. The problem is as follows: Two cards from an ordinary deck of 52 cards are missing. What is the probability that a random card drawn from the deck is a spade? For…
mattpolicastro
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Solving a multiple choice question paper

Firstly, I am not sure whether this is a mathematical problem. Please inform me in case it is not. My question is as follows I have a online game with 14 questions. It's a kind of treasure hunt. Each question has 4 choices. The correct answer…
Harish
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