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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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Probability of a two-headed coin given a few sample flips?

A probability problem was posed to me, and I am terrible at probability. It was first posed to me like this: I have 5 coins. One of them is a two-headed coin, and the others are normal coins. I pick a coin, and then I flip that coin three…
Ricket
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Delta Function as The Probability Distribution Function.

When a random variable $X$ has only one possible outcome $x_0$, the probability density function at $X=x_0$ is infinite, while the probability density at other locations is zero. Then the p.d.f is exactly a delta function $\Pr(X=x) =…
Strin
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Find the unfair coin

I've had some fun thinking about these (and related) problems, but things get very complicated very quickly, and I constantly doubt my own work! I would like to see what others do with them. Thanks! You have two identical-looking coins, but one is…
Matt E
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"Standard error" of a sample's 90th percentile for a normally distributed population

When sampling from a normally distributed population, I understand that the expected deviation between the sample mean and the population mean can be calculated using the standard error $$ \text{standard error} =…
kilojoules
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Gambling device: What's my probability to win at 5 dollars before going bankrupt?

I'm going gambling and I have ten dollars. I have a gambling device that costs 1 dollar per game to play. I win with a probability of $\frac{1}{5}$ and each win gives me back four dollars (to a net profit of three) while lost games give nothing back…
kviiri
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If $P(A \ \cup \ B) = P(A) + P(B)$, is it the case that $A$ and $B$ are disjoint?

I know that if $A$ and $B$ are disjoint events, then $P(A \cup \ B) = P(A) + P(B)$. However, is the converse true as well? Thanks.
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Probability of "L" shape on chessboard

If three one by one squares are drawn from the chessboard then the probability that they form the letter "L" is? I was thinking that if we select a 4 sided square is selected it will contain an "L".Am i going on right track?Please help!
user220382
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How many tosses for 95% centainty that coin is not fair

Given a bag of 10 coins, 9 are ordinary coins and one is a double headed coin. You select one coin at random and toss it three times. It comes up heads each time what is the probability its the double header? This can be solved using bayes rule the…
Bazman
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Given n raffles, what is the chance of winning k in a row?

I was reading this interesting article about the probability of of tossing heads k times in a row out of n tosses. The final result was $$P = 1-\frac{\operatorname{fib}_k(n+2)}{2^n}\;,$$ where $\operatorname{fib}_k(n)$ is the $n$-th $k$-step…
Oak
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Arranging items in strictly increasing order

"We throw 3 dice one by one. What is the probability that we obtain 3 points in strictly increasing order"? Isn't the answer just $1/6$ as there are $3!$ possible permutations and only 1 permutation in which the 3 dice will be in strictly increasing…
Jojo
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Flipping $n$ coins in a circle until they are all gone

You have $n$ coins arranged in a circle, labeled $1$ to $n$. You start at the first coin and go around. At each coin you flip it - if it lands heads you keep it, if it lands tails you remove it. Which coin is most likely to be the last coin…
MT_
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Probability that a coin lands on tails an odd number of times when it is tossed $100$ times

A coin is tossed 100 times , Find the probability that tail occurs odd number of times! I do not know the answer, but I tried this, that there are these $4$ possible outcomes in which tossing of a coin $100$ times can unfold. head occurs odd…
Tomarinator
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Probability that on three rolls of dice, there will be at least one 6 showing up?

What is the probability that on three rolls of dice, there will be at least one 6 showing up? Attempt: Since there can be one six or two sixes or three sixes on three rolls, I considered separate cases and added them up. So $(1/6)(5/6)(5/6) +…
Taylor Ted
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simulating a fair six with a four equal sector spinner

Whist teaching basic probability I needed a group to use a fair four sector spinner but I'd none left. I gave them a die asking them to disregard 5,6 should they arise. The problem got me thinking about what I could do if I needed a die and only…
Karl
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Probability of winning the lottery the more you play it?

Recently I was having a conversation with a philosophy student on gambling and it intrigued me because of what the person was saying. Before I say what the person said, I remember learning in class that the probability of something occurring does…
Belphegor
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