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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 .

105859 questions
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probability of being dealt four of a kind in poker

I have to resolve this exercise: I have 52 cards. I get 5 cards. Calculate the probability I get a poker hand of four-of-a-kind. well I applied the formula ${52 \choose 5}=\frac{52!}{5!47!}$ to calculate every possible combination.but after here I…
Mazzy
  • 281
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The Lost Boarding Pass Advanced

The Lost Boarding Pass is a famous puzzle as follows: On a sold out flight, $100$ people line up to board the plane. The first passenger in the line has lost his boarding pass, but was allowed in, regardless. He takes a random seat. Each subsequent…
gurtonn
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$X_1, \dots, X_n$ are independent random variables. Suppose $M = \min(X_1, X_2, \dots, X_n)$

Given that $X_1,\dots, X_n$ are independent random variables. Suppose $M = \min(X_1, X_2,\dots, X_n)$ and $X_i$ are exponential random variables with parameter $λ_i$, compute $E[M X_j | M = X_i]$ where $i \ne j$. I have got the pdf and pmf of $M$.…
Euclid Ye
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Probability of A given B given C

How would I find P ((A|B)|C)? Do I substitute the formula for P (A|B), P=(A ∩ B))/(P (B)), and then redo the function to get (P (A ∩ B ∩ C))/(P (C)^2)? I heard that P=(A|B ∩ C) can be used, but why would that be equivalent, unless you assume that C…
Katie Tibbs
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Comparing the probabilities of rolling a $12$ or two consecutive $7$'s first with a pair of dice

A pair of dice is rolled repeatedly which event is more likely to occur first? Event $A$ both dice shows 6's. Event $B$ two consecutive rolls give a sum of 7 each. By not solving I think it's A since it's more likely to happen since your just…
Devaraja
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Does equality in distribution imply equality of expected value?

In other words, if X = Y in distribution, is it true that EX = EY? I think this must be true, but I've tried to prove it a few times and I always get stuck. Thanks in advance for any hints or reference.
Not Durrett
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Probability question - tagging birds and then determining total number based on how many are tagged

I tag 10 birds, and then release them into the wild. I decide to catch the birds until I catch 10 birds that I haven't tagged yet. If I catch 12 birds, what is an estimate for the total number of birds in the wild? My preliminary guess is 10/2 * 12…
Kevin
  • 319
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Expected rolls to get 3 of any number

Suppose I am rolling a die repeatedly, and I keep a tally of how many times each number has come up. As soon as a number has come up 3 times, the game is over. It does not need to be 3 times in a row - the tally just needs to reach 3. What is the…
jwd
  • 463
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Probability that binomial random variable is even

Suppose $X$ is binomial $B(n,p)$. How can I find the probability that $X$ is even ? I know $$P(X = k ) = \frac{ n!}{(n-k)!k!} p^k(1-p)^{n-k} $$ where $X=1,....,n$. Are they just asking to find $P(X = 2m )$ for some $m > 0$ ?
user203867
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Expected number of steps to transform a permutation to the identity

Start from an identity permutation P=[1,2,3,4,5], each step choose two random integers k and l in [1,5]. Then swap P[k] and P[l]. Stop the process until P again becomes identity. Observe that the expected number of steps is 120. I can not prove…
user12290
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Is it highly unusual to win a lottery with 10 tickets in 6 weeks out of 7?

A woman in my local Rotary Club has won our weekly drawing 6 out of 7 weeks and I wanted to know the actual odds of this happening. On average 10 tickets are bought which I know makes her daily odds $1/10$. How to find the odds to win 6 out of 7?
Joe Roberts
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How can I solve this using permutations?

Delegates from 10 countries, including Russia, France, England and the United States are to be seated in a row. How many different seating arrangements are possible if the French and English delegates are to be seated next to each other and the…
RXY15
  • 911
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Choosing exactly 2 damaged pieces (Probability)

From $27$ pieces of luggage, an airline handler damages a random sample of $4$. The probability that exactly one of the damaged pieces of luggage is insured is twice the probability that none of the damaged pieces are insured. Calculate the…
Jimmy Hoang Huy Nguyen
  • 111
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Making triangles out of a triangular lattice?

First off: Yes, I am well aware that this question has been posted before. However, the answer in that one was incorrect, so I decided to make another thread to gain more input, as well as provide what I have figured out on the problem so far. The…
Mathy Person
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What is the probability of two out of three events happening?

All events are independent. $$\Pr(A) = \frac{9}{10}$$ $$\Pr(B) = \frac{9}{10}$$ $$\Pr(C) = \frac{6}{10}$$ What is the probability of at least two events happening? I'd like to use negation, to negate the possibility that event no event happen plus…
lzc
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