Jun 20, 2016 · Two events are disjoint, or exclusive, if their intersection is an empty set, which in turn infers it to have zero probability. The intersection of disjoint events is impossible. The intersection of disjoint events is impossible.

As per the definition random variable, the values the random variable can take should follow a determinable distribution. Hence this disjoint random variable may mean that the distributions of the two variables from which the two subsets are drawn from. Further the subsets themselves may be disjoint.

Mar 5, 2023 · $\begingroup$ I'd first calculate the probability that sequence a has k distinct terms, with the binomial distribution. Then for a given k, it's easy to calculate the probability that sequence b is disjoint, which is $ P(b_1 \notin a )^m$ is $\endgroup$ –

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$\begingroup$ Technically, an event of probability 0 is independent of any other event, and it could also be disjoint from the other event. $\endgroup$ – Daniel Schepler Commented Jan 24, 2018 at 19:07

May 2, 2017 · Disjoint $\Rightarrow$ Dependent is not logically equivalent to . Not Disjoint $\Rightarrow$ Not Dependent. What you have, however, is that it is logically equivalent to. Not Dependent $\Rightarrow$ Not Disjoint. This is a special case of a general rule which asserts that a conditional statement is logically equivalent to its contrapositive.

Mar 7, 2018 · Two events are mutually exclusive if the probability of them both occurring is zero, that is if $\operatorname{Pr}(A \cap B) = 0$. With that definition, disjoint sets are necessarily mutually exclusive, but mutually exclusive events aren't necessarily disjoint. Consider points in the square with each coordinate uniformly distributed from $0$ to ...

Jul 25, 2014 · Solving for the probability of an disjoint event. 0. Need assistance with conditional probability problem. 0.

Sep 22, 2020 · $\begingroup$ The statements “disjoint events with positive probability are not independent” and “independent events with positive probability are not disjoint” are equivalent statements. You have proven the first statement, therefore the second one is true. $\endgroup$

Probability of two disjoint events but the probability of one event is unknown. 1.