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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What is the probability that $7$ cards are chosen and no suit is missing?

Cards are drawn one by one from a regular deck ($13$ cards for each of the $4$ suits). If $7$ cards are drawn, what is the probability that no suit will be missing? Ok, so I tried the approach where I choose the $1$ suit out of $4$ and then I…
ahrnad
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Average distance between two points on a unit square.

Consider the unit square $S =[0,1]\times[0,1]$. I'm interested in the average distance between random points in the square. Let $ \mathbf{a} = \left< x_1,y_1 \right>$ and $ \mathbf{b} = \left< x_2,y_2 \right>$ be random points in the unit square. …
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a question related to two competing patterns in coin tossing

If I have a two-sided coin with probability $p$ showing head. I repeatedly toss it until either HTHTH or HTHH appears. Can you calculate 1) the probability when I got HTHTH, and 2) the expected value of the number of tosses before I stop? Thanks.
Qiang Li
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Expected number of rolls to get all colors on 6-sided die colored in with 3 colors

If I have a die that has 3 red sides, 2 blue sides, and 1 green side, how many rolls do I expect until every color has appeared at least once? I have run some tests and I’m getting numbers around 7.31, but clearly I’m looking for a mathematical…
Stephen
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How many times $n$ must you play a game in which you have a $1/N$ chance of winning to have a better than 50% chance of winning at least once

I am having difficulty approaching the above problem, and would like a hint. I tried doing an inclusion exclusion argument: Let $A_{i}$ be winning the game on the i'th try, then by inclusion exclusion we have, for winning at least 1 game in n…
operatorerror
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How to calculate intersection and union of probabilities?

lets say I have a switch A with 3 legs, each leg has 0.8 chance to be connected (and then electricity will flow), we need only 1 leg connected for A to transfer the electricity (so sorry I didn't explain it that well I'm having hard time to…
The One
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Probability of drawing cards in ascending order

Given 200 cards where each card has a unique number from 1 to 200. We randomly pick 30 cards (the order we pick them matters). What is the probability the unique numbers of the cards we pick are in ascending order?
MATH000
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Find the probability the largest number appearing on the coupon is 9.

15 coupons are numbered 1,2,3...15. 7 coupons are selected at random one at a time with replacement. Find probability that 9 is the largest number appearing on the coupon. I am having a problem finding $N(a)$ for this problem. My working: $N(s)=…
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What does probability really mean?

I apologize in advance if the question is a bit off-topic and not strictly mathematical. To be clear, I'm talking about classical probability which is defined like this: Given a finite sample space $S$, and a subset of $S$ which we call event $E$,…
Omar Nagib
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Probability of picking 3 numbers in sequence, with k random picks

I am struggling a bit with this problem, I think I am somehow close but I miss something. Let's assume we have numbers from $1$ to $30$, we pick $5$ random numbers (with repetition) and we want to know the probability to pick at least $3$ numbers in…
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Flipping fair coin -

Examining an event. Let's say we flip a fair coin many times. Let's say 1.000.000 times. We know that even though each flip is not connected, influenced by past or future flips, in the long run each side heads or tails will end up approximately…
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100 coins problem

100 coins in a circle, clockwise labeled 1-100. Starting at coin 1, you flip each one moving clockwise. If a coin lands tails, you keep it, if it lands heads, you remove it. After a long time, only one coin will remain. What would you expect its…
szd116
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How do we formally distinguish between zero probability events that may and may not actually occur?

Consider a random variable $X$ with pdf \begin{equation} f(x)= \begin{cases} 3/2 &\text{ if } x\in[0,1/3]\cup[2/3,1] \\ 0 & \text{ otherwise} \end{cases} \end{equation} Here, $P(X=1/6)=P(X=1/2)=0$, but $1/6$ and $1/2$ are somehow different, because…
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Estimate total song ('coupon') number by number of repeats

If shuffle-playing playlist ×100 resulted in [10 13 10 3 2 2] different songs being repeated [1 2 3 4 5 6] times, what is the estimate for the total number of songs? (assuming shuffle play was completely random) Update: (R code) k <- 50 # k…
ajo
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Basic probability problem

Problem states: Consider two events $A$ and $B$, with $P(A) = 0.4$ and $Pr(B) = 0.7$. Determine the maximum and the minimum possible values for $P(A \& B)$ and the conditions under which each of these values is attained. To solve, I considered the…