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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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3 balls drawn from 1 urn - probability all same color (with/without replacement)

An urn contains 5 red, 6 blue and 8 green balls. 3 balls are randomly selected from the urn, find the probability that they are all of the same color if: (a) the balls are drawn without replacement; (b) the balls are drawn with replacement.
user60991
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Urn Probability Problem containing algebraic variables

Urn A contains $x$ red marbles and $y$ white marbles, and Urn B contains $z$ red marbles and $v$ white marbles. If a marble is drawn from Urn A and put into Urn B and then a marble is drawn from Urn B, what is the probability that the second marble…
herashefat
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Understanding Conditional Probability (Math is Fun)

I have trouble understanding a simple concept from Math is Fun. STATEMENT: 70% of your friends like Chocolate, and 35% like Chocolate AND like Strawberry. What percent of those who like Chocolate also like Strawberry? SOLUTION:…
ArnuldOnData
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How long will it take to get 10 heads in a row flipping coins?

I need a way of solving this problem: It's not math homework, I legitimately want to know and it's bothering me. So the probability of having a coin land on heads is .5 or 1/2, so it'll land on heads half the time in a perfect world. The…
Nick
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Probability of Winning Election if Outcomes not Equally Likely

I just started learning probability, so my level is not very high. I am doing a homework problem, and my answer is different than the book's. I can't understand why. I see how the answer in the book makes sense, but I also see how my procedure makes…
SebastianLinde
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Probability - four random integers between 0-9, that not more than two are the same

Four integers are chosen at random between 0 and 9, inclusive. Find the probability that (a) not more than 2 are the same. What I tried: all unique numbers: 63/125, two same numbers: 72/1000 And then add them both. But the answer…
user585380
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Why isn't the probability that Alice will have classes every weekday $\dfrac{5\times \binom{5}{2}}{30\choose 7}$?

Blitzstein's Introduction to Probability (2019 2 ed) Ch 1, Exercise 54, p 51. Alice attends a small college in which each class meets only once a week. She is deciding between $30$ non-overlapping classes. There are $6$ classes to choose from for…
Aniruddh Shekhawat
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Find expected value of last roll

Suppose that you play the following game: You roll a fair die at most $N$ times and get an amount of dollars equal to the last number rolled. You can decide to stop the game at any time. What is the (approximate) value of this game for $N=60$? Here…
Ted
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Expected intersection size of two random sets

There are two sets, $A=\{a_1, \dots, a_n\}$ and $B=\{b_1, \dots, b_m\}$, for some $m$ and $n$. The elements $a_1, \dots, a_n$ and $b_1, \dots, b_m$ are all $x$-bit binary strings, and they are all uniformly sampled from $X$, which is defined as the…
user4478
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Probability of getting 6 k times in a row

What is the probability of getting $6$ $K$ times in a row when rolling a dice N times? I thought it's $(1/6)^k*(5/6)^{n-k}$ and that times $N-K+1$ since there are $N-K+1$ ways to place an array of consecutive elements to $N$ places.
Lazar Šćekić
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Precisely defining the conditional distribution of $X$ given that $Y = y$

Let $(\Omega,\Sigma,P)$ be a probability space and let $X\colon \Omega \to \mathbb R$ and $Y\colon \Omega \to \mathbb R$ be continuous random variables with density functions $f_X$ and $f_Y$, respectively. I would like to precisely define the…
eternalGoldenBraid
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Intuitive understanding of conditional density $f_{X \mid Y}(x \mid y)$

Let $X$ be a continuous random variable with probability density function $f_X$. The way that I think about the meaning of $f_X$ is this: if $\Delta x$ is a small positive number then $$ P(X \in [x,x+ \Delta x]) \approx f_X(x) \,\Delta x. $$ Now…
eternalGoldenBraid
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What is the probability that you chose the coin B

Question Suppose you have two coins A and B the probability of head in A is $\frac{1}{4}$ and the probability of head in B is $\frac{3}{4}$. Now, suppose you have chosen a coin and tossed it two times. The output was head and head. What is the…
laura
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Law of Total Probability (Lecture 110 Harvard)

I was watching Harvard STAT 110 lecture series on Youtube. As per lecture 10, given $$T=X+Y$$ I have the following question: Why is $$P(T=t) = \sum P(T=t|X=x)\ P(X=x)$$ and not $$\sum P(T=t|X=x)\ P(X=x)+ \sum P(T=t|Y=y)\ P(Y=y)?$$
Anisha Jain
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Calculate $\mathbb{E}[F(Y)]$

I try to resolve this problem, but I have some difficulties to get a clear result. The problem : Let X be a normal random variable with mean 0 and variance 1 (ie. $X\sim \mathcal{N}(0,1)$). Let Y be a normal random variable with mean $m$ and…
Gauss
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