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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Total probability of a match, where first to $n$ games wins.

In a match between two players A and B, the first to win $n$ games wins the match. Player A wins a game with probability $p$, the outcomes of each game are independent. (The probability of player B winning a game is $q=1-p$.) I've found that the…
Teddy38
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Binomial-Like Distribution with Changing Probability

The Question Assume we have $n$ multiple choice questions, the $k$-th question having $k+1$ answer choices. What is the probability that, guessing randomly, we get at least $r$ questions right? If no general case is available, I am OK with the…
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Expected time before Farmer Brown is abducted?

Farmer Brown is standing in the middle of his perfectly circular field feeling very content. It is midnight and there is no moon and unknown to the farmer, Martian zoologists are landing randomly at points on the circumference of his field. They…
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Expected number of offers until house is sold

I am selling my house, and have decided to accept the first offering exceeding $K$ dollars. Assuming that offers are independent rv with common distribution $F$, find the expected number of offers received before I sell the house. Try I call $X$…
James
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Find the probability that the pedestrian has to wait for exactly $4$ seconds before starting to cross.

From Statistical Inference (2nd edition) by Casella Berger The flow of traffic at certain street corner can sometimes be modelled as a sequence of Bernoulli trails by assuming that the probability of a car passing during any given second is a…
JoZ
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Expected value of playing a game

A game has probability $\frac13$ of winning. Someone would like to play this game and continue to play until he loses two in a row. What is the expected number of playing the game?
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What is the probability that some random event won't happen in the next 10 minutes given it happened exactly twice in the last 120 minutes?

The title says pretty much all. The event is fully random, it has the same chance any minute, it can happen multiple times at the same minute. How is it possible to calculate that? I made a simulation code in c++, which says 78%, is that good…
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Find a probability mass function of a random variable

$\color{red}{Attempt} $ We start with $k=1$, $P(X=1)$ is the probability that one letter have been put in the correct envelope. Our sample space size is $n$ and since there is only one way that one letter must have been put into the correct…
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What numbers in $[0,1]$ can be generated by tossing a fair coin?

What numbers in the interval $[0,1]$ can be generated by tossing a fair coin? By generating a number using a coin, we mean finding an event that its probability is the given number. I think that any number in $[0,1]$ can be generated by tossing…
stressed out
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Probability that exactly 2 balls are white

What I did. I let $X$ be number of withdraws before $x$ white balls. We can call our succes in this case to be gettin a white ball and probability is of course $p = \frac{3}{6} = \frac{1}{2}$. So we see $X$ is negative binomial r.v with $n=4$…
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Probability that a 5 occurs first

Suppose we roll pair of dice until a sum of either 5 or 7 appears. What is the probability that a sum of 5 occurs first? Try: Let $A$ be the event that a sum of $5$ occurs on the ith roll and $B$ that the sum of 7 occurs on the ith roll. We are…
James
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Drunk men finding their tents

Problem: There are four couples camping at the lakeside. They start drinking and as the women get bored and tired, they all go to sleep into their tents. The men continue and get very drunk. In the morning they all go randomly into a tent (but each…
malasi
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What is the expected number of boys?

If the probability that a child is a boy is $p$, find the expected number of boys in a family with $n$ children given that there is at least one boy? My answer: My friend says the answer is $np+q$ but my answer is $np/(1-q^n)$. I found my answer…
user90596
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What's the probability of 2 credit card numbers matching, given incomplete data and known expiry date?

Trying to settle an office argument on a challenging probability scenario, thought I'd see if anyone would like to take a stab: We're trying to determine the probability of 2 credit cards matching amongst a global population given that only the…
contool
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shoes probability for finding exact k pairs of shoes

The closet has $10$ pairs of shoes. The no. of ways in which $6$ shoes can be choosen from it show that There will be (i) no Complete pair (ii) exactly one complete pair (iii) 2 complete pair (iv) 3 complete pair My Try: Total no. of selecting $6$…
juantheron
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