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Questions tagged [conditional-probability]

For questions on conditional probability.

Conditional probability is the probability that an event occurs given that another event has already happened. The probability of an event $A$ given another event $B$ is written as $P(A|B)$, and is related to the marginal and joint probabilities via $$ P(A|B)P(B)=P(A\cap B)$$

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Urn Problem (Conditional Probability)

There are two Urns, Urn $A$ and Urn $B$. In Urn $A$ there are $3$ red marbles and $2$ blue ones. In Urn $B$ there are $2$ red marbles and $3$ blue ones. Through a fair coin toss we select one of the Urns and draw two marbles from it consecutively…
J. Hodge
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probability conditioned on everything

what is the probability $\sum_i P(A|B_i)$ given the $\cup_i B_i = \Omega$, where $\Omega$ represents all possible events? Many thanks, A.
altroware
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If it's known that the 4 cards have different ranks, what is the probability that the first card is a spade?

First, I choose the spade; 13 ways. Then throw away the other 3 cards of that rank. From the remaining 48 cards I choose 1, and throw away the other 3 cards of that rank. From the remaining 44 cards I choose 1, and throw away the other 3 cards of…
Chesso
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two fair dice are rolled

two fair dice are rolled, what is the probability their sum is a 10 given that the first roll is a 6? not sure why i can't solve this simple problem. i presumed the following: A: event that sum is 10 B: event that first roll is 6 $$Pr(B) =…
rocketboy2000
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DNA test at scene of crime

A DNA sample has been taken at the scene of the crime. Statistically, the probability of an arbitrary individual's DNA profile to coincide with the one taken at the scene is 0.000001 (0.0001%, i.e. one in a million). A DNA test is carried out among…
user805623
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Conditional probability Question: $G\sim \operatorname{Geom}(p)$ Show that for any $k, l\ge 0, P(G > k + l|G > k) = P(G > l).$

$G\sim \operatorname{Geom}(p)$. Show that for any $k, ℓ ≥ 0$, $$ P(G > k + ℓ|G > k) = P(G > ℓ). $$ So, for this I equated both formulas but replaced the powers but I don't know what happens to the $p$ in the formula. $$ ((1-p)^{k+l}/(1-p)^k) =…
user639649
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Conditional Probability for Chocolates Shipped on Time

Question: The probability that an order of chocolates ships on time is 0.70. The probability that an order is shipped on time and delivered on time is 0.56. What is the probability that such an order will NOT be delivered on time, given that it…
rbharat01
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Football League coincidence

In the English Championship division, there are 24 teams, 8 of which have names starting with the letter B (e.g.Brighton) Tonight, all 24 teams in this division are playing each other. By a coincidence, the 8 teams starting with B are playing each…
user67005
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$B \cap\ C$ = $\phi\ $ and $D = B^c \cap C^c$, does the collection of the events B,C,D form a partition?

Looking for a bit of help here. If $B$ and $C$ are disjoint, and $D = B^c \cap C^c$ does that make D=1 and therefore they would form a partition? I think it cannot be that simple. The full question also includes the following. Events $A,B,C,D$…
fresh143
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Distribution of function given the variable

Suppose $\theta \sim N(\mu, \sigma)$ and $Y = f(\theta) = \theta^2 + w$ with $w \sim N(0, \sigma_w)$. Obviously $p(Y)$ is not Gaussian, as $f$ is nonlinear in $\theta$. My question is: Is $p(Y|\theta)$ Gaussian distributed? I assume it is, because…
omg
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Picking a specific domino last

My family recently had a domino game (double 12 set = 91 unique) in which each of 5 players started with 10 in their hand. We needed to start the game with the double "1", but no one had it. Everyone took turns and continued to draw for the double…
KCRJ
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Conditional Probability(MIT Assignment)

Oscar has lost his dog in either forest A (with a priori probability $0.4$) or in forest B (with a priori probability $0.6$). On any given day, if the dog is in A and Oscar spends a day searching for it in A, the conditional probability that he will…
Diya
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Joint conditional distribution

Hey I have a question where i think i am doing everything correct but I don’t get the expected solution, I think the solution may be wrong - or I am.... Calculate P(0I1) and P(1I1) for $$P(X=1|Y=1) =P(X=1,Y=1)/P(Y=1)=0.3/0.5=3/5$$ And $$P(X=0|Y=1)…
Lillys
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Conditional probability : $\mathbb P\{X\in A, Y\in B\}=\mathbb P\{X\in A\mid Y\in B\}\mathbb P\{Y\in B\}=\int_B\mathbb P\{X\in A\mid Y=t\}f_Y(t)dt$?

I'm confuse on some probability formula with conditional probability. I know that $$\mathbb P(A\cap B)=\mathbb P(A\mid B)\mathbb P(B).$$ Let $X,Y$ two (continuous) random variable. Then, $$\mathbb P\{X\in A,Y\in B\}=\mathbb P\{X\in A\mid Y\in…
user621345
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using Bayes’ Rule to calculate conditional probability

i have following problem, "Students who party before an exam are twice as likely to fail the exam as those who don't party (and presumably study). Of 20% of students partied before the exam, what percentage of students who failed the exam went…
Nour
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