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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How to determine if coin comes up heads more often than tails?

Not a math student, so forgive me if the question seems trivial or if I pose it "wrong". Here goes... Say I'm flipping a coin a n times. I am not sure if it's a "fair" coin, meaning I am not sure if it will come up heads and tails each with a…
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If you draw two cards, what is the probability that the second card is a queen?

We had this question arise in class today and I still don't understand the answer given. We were to assume that drawing cards are independent events. We were asked what the probability that the second card drawn is a queen if we take two from the…
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Expected value of maximum of two random variables from uniform distribution

If I have two variables $X$ and $Y$ which randomly take on values uniformly from the range $[a,b]$ (all values equally probable), what is the expected value for $\max(X,Y)$?
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Probability of 3 Heads in 10 Coin Flips

What’s the probability of getting 3 heads and 7 tails if one flips a fair coin 10 times. I just can’t figure out how to model this correctly.
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What is the probability of a coin landing tails 7 times in a row in a series of 150 coin flips?

If you were to flip a coin 150 times, what is the probability that it would land tails 7 times in a row? How about 6 times in a row? Is there some forumula that can calculate this probability?
Chuck
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In need of tips/suggestions when to add or multiply probabilities

I am having trouble deciding when to add or when to multiply probabilities as in the following example. I know that by constructing Probability tree diagrams we could multiply along branches and add vertically. However I could definitely use more…
MistyD
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If I have a $0.00048\%$ chance of dying every second, how to numerically calculate the chance I have of dying in a day?

Hypothetically, if I have a 0.00048% chance of dying when I blink, and I blink once a second, what chance do I have of dying in a single day? I tried $1-0.0000048^{86400}$ but no calculator I could find would support this. How would I work this…
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A family has three children. What is the probability that at least one of them is a boy?

According to me there are $4$ possible outcomes: $$GGG \ \ BBB \ \ BGG \ \ BBG $$ Out of these four outcomes, $3$ are favorable. So the probability should be $\frac{3}{4}$. But should you take into account the order of their birth? Because in that…
Niharika
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Expected number of loops

There are 100 ropes in a bag. In each step, two rope ends are picked at random, tied together and put back into a bag. The process is repeated until there are no free ends. What is the expected number of loops at the end of the process?
n0vakovic
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What is the probability that eventually it will rain forever?

Probability of raining today is 60%. If it rains today, the probability of raining tomorrow will increase by 10%. If it doesn't rain today, the probability raining tomorrow will decrease by 10%. Rule 2 and 3 can be applied to future days. What is…
Leslie Sun
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Probability of being poisoned

You are playing a game in which you have $100$ jellybeans, $10$ of them are poisonous (You eat one, you die). Now you have to pick $10$ at random to eat. Question: What is the probability of dying? How I tried to solve it: Each jellybean has a…
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Basic Probability Help for First Year Teacher

Need some help. I'm a first year teacher, moving into a probability unit. I was looking through my given materials, and think I've found two errors. It's been a long time since I've done probability and I don't want to ask staff for fear of sounding…
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Why is the expected value $E(X^2) \neq E(X)^2$?

I wish to use the Computational formula of the variance to calculate the variance of a normal-distributed function. For this, I need the expected value of $X$ as well as the one of $X^2$. Intuitively, I would have assumed that $E(X^2)$ is always…
Nova
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Three coins are tossed. If one of them shows a tails, what is the probability that all three coins show tails?

To solve the following problem Three coins are tossed. If one of them shows a tails, what is the probability that all three coins show tails? I tried $1\cdot\frac12\cdot\frac12$ where $1$ is the probability for the first coin that shows tails,…
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Prove that if events A and B are independent, then the complement events of A and B are also independent.

I know that: $$\begin{gathered}P\left(A\cap B\right)=P\left(A\right)P\left(B\right)\\ P\left(A^{C}\right)=1-P\left(A\right)\\ P\left(B^{C}\right)=1-P\left(B\right) \end{gathered} $$ My proof so far: $$\begin{gathered}P\left(A^{C}\cap…