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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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Determine the probability

Joe, who owns a grocery store, has ordered tins of chickpeas and lentils. When unpacking the tins, he finds that one box contains 10 tins that have lost their labels. The tins are identical but after looking through his invoices, he has determined…
Justine
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Lottery - Probability

Looking over Canada's Western Lotto Max and Daily Grand lottery probabilities, a combinations calculator shows the actual chance of getting 7/7 with 50 numbers is 1 in 99,884,400. However, that's if you only had 1 selection per ticket. Since there…
Cannon444
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If $S_n$ is Binomial $(n,p)$ then $\mathbb P(S_n=k)\approx \frac{(np)^k}{k!}e^{-np}$.

I was reading this post, and I have to admit that I was quite confused. The question was : If $S_n$ is a Binomial r.v. with parameter $(n,p)$ s.t. $n$ large, $p$ very small and $np$ not to big (for instance $np\leq 10$), then $$\mathbb…
user659895
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Probability random coins tossing

You are playing with a friend: You are tossing a (fair) coin. If it is a tail, you win. If not, then you are tossing 2 (fair) coins. If they are both tails, you win. If not, you are tossing 3 (fair) coins, if they are all tails you win. If not, you…
Joshua Haim Mamou
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Let $\lambda \in \mathbb{R}, \lambda > 0$ and let $X, Y, Z \sim P(\lambda)$ (they have Poissons distribution) independent random variables..

Let $\lambda \in \mathbb{R}, \lambda > 0$ and let $X, Y, Z \sim P(\lambda)$ (they have Poissons distribution) independent random variables. Calculate $Var (XYZ) $. I tried by calculating $ \mathbb{E} (XYZ) ^2 ( = \lambda ^6)$ because $X,Y,Z$ are…
user560461
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justification of $\operatorname {E} \left[2X\operatorname {E} [X]\right] = 2\operatorname {E} [X]\operatorname {E} [X]$

I am learning Variance. $${\displaystyle {\begin{aligned}\operatorname {Var} (X)&=\operatorname {E} \left[(X-\operatorname {E} [X])^{2}\right]\\[4pt]&=\operatorname {E} \left[X^{2}-2X\operatorname {E} [X]+\operatorname {E}…
brennn
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Probability of failing 2 out of the last 3 consecutive trials

In a test with a series of trials, you'd fail the test if you fail 2 out of the last 3 trials (i.e. window of 3). For example, for a series of trials (starting from index 0, 1, ..., 7), we have results: 0, 1, 0, 0, 0, 1, 0, 1 (Fail is 1, Not failing…
Jessie Vivienne
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Chance of getting a good grade

Lets says theres a question bank of 28 questions. On the exam, there will be 12 of these questions, and I will have to answer 5. If the only way to get a question right is to study it, how many questions should I study to have a reasonable chance…
zzzzzzzzzzz
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If the probability of a dog barking one or more times in a given hour is 84%, then what is the probability of a dog barking in 30 minutes?

Poorly worded title but I don't know what the nature of this probability question is called. I was asked a question: If the probability of a dog barking one or more times in a given hour is 84%, then what is the probability of a dog barking in 30…
Doug Fir
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Two boys pick a subset of $40$ toys that they like. They can pick the same ones. What is the probability that they picked three same toys or more?

Two boys pick a subset of $40$ toys that they like. They can pick the same ones. What is the probability that they picked three same toys or more? My answer would be $$\frac{ \sum_{ i =3}^{40} \binom{40}{i} 3^{40-i}} { 2^{40} 2^{40}}.$$ Is that…
user15269
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Probability of at least two events occurring.

The proportion of the American adult population that supports candidate Green is p=0.22. A SRS of 9 adults asks if they agree with the statement “I support candidate Green.” What is the probability that at least 2 of those surveyed would agree…
Evan Marsh
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Free throws in basketball game about probability

Someone shoots free throws. He/She made the first one and missed the second one. From the third shot, the probability of hitting the ball equals to the free throw percentage he/she made before it. For example, if the made 87 out of 100 tries. Then…
YellowRiver
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A simple problem. What am I doing wrong?

I am totally new to probability and I am a little bit confused. I have the following homework: A large group of people are competing for all-expense-paid weekends in Philadelphia. The Master of Ceremonies gives each contestant a well-shuffled deck…
Steve Cheng
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How do you compute the steady state probabilities of a continuous time markov chain?

Given a markov model with transition rate matrix $Q$, where the probability of each state at time $t$ is given by $P(t) = P(0)e^{Qt}$, where e is the matrix exponential, the steady state probabilities should be given by taking the…
bmillare
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If $A\subseteq B$, can $A$ and $B$ be independent?

I know that in probability theory, to say that two events are independent means that the occurrence of one does not affect the probability of the other. But if $A$ is a subset of $B$, then $A$ and $B$ are not independent right? Also I do not…
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