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Recent questions in Mutually Exclusive Events

beatricalwu 2022-07-21

Let $A$ =event space. Assume that ${A_{n}}$ is a monotone nondecreasing sequence of events in A $A$ . Let ${A_{n}}$ be a sequence of sets defined as follows:
$B_{1} = A_{1}; B_{i} = A_{i} - A_{i - 1} for i \in {2, 3, 4, \dots}$
Prove that ${B_{n}}$ is a sequence of mutually exclusive events in $A$ . Justify each line of proof.
I know that what I need to show here is $B_{i} \cap B_{j} = \emptyset$ for any $i < j$ . I've divided it to be proof by cases where case $1$ is $i = 1 and j \in {2, 3, 4, \dots}$ and case $2$ is $i \in {2, 3, 4, \dots}$ and $j \in {2, 3, 4, \dots}$ where $i < j$ so that $B_{i} = A_{i} - A_{i - 1} and B_{j} = A_{j} - A_{j - 1}$ and $B_{i} = A_{i} - A_{i - 1} and B_{j} = A_{j} - A_{j - 1}$ where $i \in {2, 3, 4 \dots}$ and $j \in {i + 1, i + 2, \dots}$ .

Lorena Lester 2022-07-20

$A \cup B$ can be expressed as the union of two mutual exclusive events in the following way:
$A \cup B = A \cup (B - A B)$
Express $A \cup B \cup C$ in a similar way.

Paxton Hoffman 2022-07-20

Find an $x$ such that mutually exclusive events are to disjoint sets what independent events are to $x$

ingwadlatp 2022-07-20

Events $A$ and $B$ are independent, events $A$ and $C$ are mutually exclusive, and events $B$ and $C$ are independent.
If $P (A) = 12; P (B) = 14; P (C) = 18$ ; what is $P (A \cup B \cup C)$ ?

Matias Aguirre 2022-07-19

Prove or disprove via proof that events X and Y can be independent and mutually exclusive if both of their probabilities are greater than 0.

Math can be challenging, but with the right help and understanding, it can be easy to understand. Mutually exclusive events are two events that cannot occur at the same time. If one event occurs, the other cannot. For example, if you are asked a yes or no question, the answer is either yes or no and not both. This concept can be used to solve equations and answer questions. At Plainmath, we understand the difficulty of understanding mutually exclusive events and are here to help. Our website is full of resources, including tutorials and practice questions, to help you understand this concept and any other math questions you may have. Don't wait, get the help you need today!

High school probability

Improve Your Mutually Exclusive Events Skills with Practice Problems and Real-World Examples

A ∪ B can be expressed as the union of two mutual exclusive events in the following way: A ∪ B = A ∪ ( B − A B )Express A ∪ B ∪ C in a similar way.

Find an x such that mutually exclusive events are to disjoint sets what independent events are to x

Events A and B are independent, events A and C are mutually exclusive, and events B and C are independent.If P ( A ) = 12 ; P ( B ) = 14 ; P ( C ) = 18; what is P ( A ∪ B ∪ C )?

Prove or disprove via proof that events X and Y can be independent and mutually exclusive if both of their probabilities are greater than 0.

$A \cup B$ can be expressed as the union of two mutual exclusive events in the following way:
$A \cup B = A \cup (B - A B)$
Express $A \cup B \cup C$ in a similar way.

Find an $x$ such that mutually exclusive events are to disjoint sets what independent events are to $x$

Events $A$ and $B$ are independent, events $A$ and $C$ are mutually exclusive, and events $B$ and $C$ are independent.
If $P (A) = 12; P (B) = 14; P (C) = 18$ ; what is $P (A \cup B \cup C)$ ?