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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 law of waiting times

Yousha takes the train every day from Jangpura, where he lives, to go to his school at INA train station. Jangpura is on the Violet line, while INA is on the yellow line and the interchange is at Lajpat Nagar station. The waiting times in…
Pradeep Suny
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> Let $X$, $Y$, and $Z$ be three independent uniform random variables on $[0, 1]$. What is $P(XY < Z^2)$?

Let $X$, $Y$, and $Z$ be three independent uniform random variables on $[0, 1]$. Compute the probability $P(XY < Z^2)$. I used the following approach : Step 1 : Calculated the Probability distribution for $XY$. It turns out to be $P(XY \leq K) =…
SmarthBansal
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Sum of Cauchy distributed random variables

Problem: Let $X_1, X_2, \ldots $ be independent $C(0,1)$ and set $S_n = \sum_{k=1}^n X_k$. Show that $\frac{1}{n}\sum_{k=1}^n \frac{S_k}{k}\sim C(0,1)$. Using the characteristic function it is easy to get that $\frac{S_k}{k}$ is $C(0,1)$. But…
Lotus3000
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Probability of having six side first

I have an exercise as follows: A and B alternately throw a dice (which has six sides numbered from 1 to 6). A starts firstly. What is the probability that A will be the first person who has side 6? Thanks for any help!
mapping
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Five people are tossing a coin ten times. What is the probability that at least 1 person gets heads 10 times?

I know that the probability that one person getting heads all ten times is 1/(2^10) or 1/1024. I also know the calculation when using "at least one" is P(At least one) = 1 - P(None). The probability of one person getting no heads is the…
acbcccdc
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Netflix profile and user probability.

So we have 4 netflix profiles in a single subscription, say 5 People have access to the account such that 1 of the person is actually piggybacking on other people's profiles. Assuming that a single show lasts about 2 hours and nobody watches more…
user37060
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probability picking parts no replacement

In a bin containing 30 parts, 27 parts are good and 3 parts are defective. a) What is the probability that if you select 3 parts randomly, without replacing the parts in the bin, from the bin that you will have 1 defective part? I thought of…
MasterYoshi
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If $Y = 1 - X$ then is the cdf of $Y$, 1 for y ≥ 1?

$$F_{X}(x)=\begin{cases} 0, & x<0 \\ x, & 0 \le x < 1 \\ 1, & x ≥ 1. \end{cases}$$ The question is contained in a text book: This is how I have proceeded: $P(y≥1) = P[(1-x)≥1] = P(x\leq 0) = 0$. I don't know how to get $1$ .
E Takly
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What is the probability that after this process the content in two bags remains unchanged?

Each of Alice and Bob has an identical bag containing 6 balls numbered 1, 2, 3, 4, 5, and 6. Alice randomly selects one ball from her bag and places it in Bob’s bag, then Bob randomly selects one ball from his bag and places it in Alice’s bag. What…
Libor Zachoval
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A Stardew Valley tree has a $20\%$ chance of growing each day. What are the odds it will grow at least $2$, $3$, or $4$ times in $d$ days?

I'm playing a game called Stardew Valley where each day, an ungrown tree has a $20\%$ chance of growing. So far I've figured out how to calculate what the odds of my tree growing at least once in d days is with the formula: $$1 - 0.8^d$$ So for…
user3169700
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Probability of getting a royal flush with four wild-cards

I am trying to calculate the probability of getting royal flush, if four 5's are wild cards that can be of any suit. I get that the probability of the first card I am picking is $\frac{24}{52}$, but then it seems to be breaking down into many…
user9569
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Probability of A given B

In high school, we were often given questions of the form: "What is the probability of A given B?" For example: What is the probability that two people were born on the same day given that one was born on a Tuesday? Intuitively, most people…
Casebash
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Calculating the probability of $ (Z-1)^2 \leq XY$

We randomly choose three numbers $X, Y, Z$ $\in [0,1]$. Calculate the probability that $ (Z-1)^2 \leq XY$. I have tried to observe just the "edge" i.e. $ (Z-1)^2 = XY$ but I am pretty much stuck on calculating the boundaries for double integral.…
user560461
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An irregular 6 faced dice

An irregular 6 faced dice is such that the probability that it gives 3 even numbers in 5 throws is twice the probability that it gives 2 even numbers in 5 throws. How many sets of exactly 5 trials can be expected to give no even number out of 2500…
Gunjan
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A probability question that involves $5$ dice

For five dice that are thrown, I am struggling to find the probability of one number showing exactly three times and a second number showing twice. For the one number showing exactly three times, the probability is: $$ {5 \choose 3} \times \left (…
Johnmgee
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