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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Permutation involving 4 cups and 4 saucers.

I study maths as a hobby. I have come across this problem: On a shelf there are 4 saucers of different colours and 4 matching cups. In how many ways can the cups be arranged on the saucer so that no cup is on a matching saucer? I start off by…
Steblo
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Probability of winning sweep stakes, put all coupons in one box or split them between boxes?

Taken from : here A mall has sweep stakes where they give you a coupon for every X dollars you spend (amount is not important). You fill the coupon with your contact details and put it in the box. Every two weeks, they draw 10 coupons, give their…
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Probability of getting a piece longer than $1/2$ on cutting a rope of length $1$ at two randomly chosen points

Here's a bootstrap approach I used to find the answer (python 3). def num_pieces(num,lenght): ot = list(range(1,lenght+1))[::-1] nig = [] for i in range(lenght-1): n = random.randint(1, num-ot[i]) nig.append(n) …
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Need help understanding formula for probability that something good happens before something bad happens.

My book says this. Consider a sequence of independent trials, each of which can be classified as good, bad, or neutral, which happen (on any given trial) with probabilities $p, q,$ and $1 − p − q$, respectively. (We do not necessarily have $q = 1 −…
user865043
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formula for relating number of successes to number of tries

Imagine we have a jar of marbles, where there are 10 different colors of marbles in the jar. Let N be the number of marbles drawn in a sample and K be the number of distinct colors in the sample. Let C be the total number of colors in the jar (which…
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Need help understanding proof for probability of union for two events.

My book says that for any two events A and B $P(A \cup B) = P(A)+P(B)-P(A\cap B)$ The proof it provides is this: $$\def\P{\mathop{\rm P}}\begin{align}\P(A \cup B) &= \P(A \setminus B) + \P(A \cap B) + \P(B \setminus A) \\[1ex]&= \P(A \setminus B) +…
user865043
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Probability Density Functions and Metropolis Hastings

I have a quick question regarding implementation of Metropolis-Hastings for a particular problem I'm dealing with. Suppose that I have a probability density function $P(X)$ for a continuous random variable $X$. In Metropolis-Hastings, I am required…
duckworthd
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The probabilty of the a 6-letter word is a palindrome

a cat is walking on the keyboard. Given that the cat walked just on letters (with an equal chance for each letter A-Z) and wrote a 6-letter word, what is the probability that this word is a palindrome.
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Using probability to determine dependent events

In my HS math class, I'm teaching Prob & Stats. We are studying how the intersection of events can show dependence. For example, we took a survey of students in the HS: 57% of those surveyed are in Extra-curricular Activities, 65% of those…
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The U.S. Senate consists of $100$ senators, with $2$ from each of the $50$ states

The U.S. Senate consists of $100$ senators, with $2$ from each of the $50$ states. There are $50$ Democrats in the Senate. A committee of size $10$ is formed, by picking a random set of senators such that all sets of size $10$ are equally likely. a)…
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probability question shooting star

There is a 91% chance of seeing a shooting star in the next hour, what is the probability of seeing a shooting star in the next half hour? chance of seeing in an hour = .91 Chance of not seeing in an hour = .09 = (chance of not seeing in a half…
Jwan622
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Uniformly at random, break a unit stick in two places. What is the probability that the smallest piece is $\leq 1/5$?

I was asked this in an interview and wasn't sure how to solve it: Consider a stick of length $1$. Select two points independently and uniformly at random on the stick. Break the stick at these two points, resulting in $3$ smaller pieces. What is…
jds
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Approximation to the monkey typewriter probability

Say that we are interested in the problem of a monkey randomly typing out a specific string of length m on a keyboard with k keys, in n trials, at least once: $$ 1 - \left(1 - \frac{1}{k^{m}}\right)^n $$ I would like to get some intuition about how…
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What is the probability that the coriander and basil are on the same side of the parsley?

Jack has seven unlabelled seeds for different herbs (coriander, basil, parsley, sage, thyme, oregano and mint). He plants the seeds in one row. What is the probability that the coriander and basil are on the same side of the parsley? I have looked…
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Treasure box with a bomb and $100 probability game

There's a treasure box with \$100. There's a 0.5 probability that the box contains a bomb. The bomb has a probability of exploding on the i-th (for $i \leq 100$) day given by a uniform distribution. The bomb will eventually explode if there is a…