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Recent questions in Mutually Exclusive Events

Rhett Guerrero 2022-11-19

Two events $E$ and $F$ are independent if any one of the following conditions are met:
(i) $P (E / F) = P (E)$
(ii) $P (F / E) = P (F)$
(iii) $P (E n F) = P (E) P (F)$
Is it correct to then assume that if $E$ and $F$ are independent having met condition (i) or (ii), then $E$ and $F$ are also mutually exclusive?

assupecoitteem81 2022-11-11

A cricket club has 15 members, of whom only 5 can bowl. What is the probability that in a team of 11 members at least 3 bowlers are selected?

cimithe4c 2022-10-28

Flipping a coin we get either head or tail can't get both so events are mutually exclusive. i.e $P (A and B) = 0$ . but flipping the same coin twice may result in either head or tail and result of flipping a coin twice is independent of what appeared the first time. So we can say events are independent?

pezgirl79u 2022-10-23

A city water supply system involved three pumps, the failure of any one of which crashes the system. The probabilities of failure for each pump in a given year are .025, .034, .02, respectively. Assuming the pumps operate independently of each other, what is the probability that the system does crash during the year?

Amiya Melendez 2022-10-22

Decide whether this statement is true or false: Let $(Ω, F, P)$ be a probability space, if for two events $A, B \in F$ $P (A \cup B) = P (A) + P (B)$ holds, then $A \cap B = \emptyset$ .

hikstac0 2022-09-30

If $\frac{1 + 3 p}{3}, \frac{1 - p}{4}, \frac{1 - 2 p}{2}$ are the probabilities of mutually exclusive events, then the set of all values of $p$ is?

Conrad Beltran 2022-09-26

List contains events $A_{1}$ , $A_{2}$ , …, $A_{5}$ which are mutually exclusive and collectively exhaustive.
Compute the following:
$\sum_{i = 1}^{k} P (A_{i}^{c})$

Nasir Sullivan 2022-09-24

If $A and B$ are mutually exclusive events, and $P (B) > 0$ , show that
$P (A | A \cup B) = \frac{P (A)}{P (A) + P (B)}$
My try:
1. We know that if $A and B$ are mutually exclusive events, then $P (A \cup B) = P (A) + P (B)$
2. We know that $P (A | B) = \frac{P (A \cap B)}{P (B)}$

gaby131o 2022-09-23

Suppose that $P (A) = 0.42, P (B) = 0.38$ and $P (A \cup B) = 0.70$ . Are A and B mutually exclusive?
from what I gather, mutually exclusive events are those that are not dependent upon one another, correct? If that's the case then they are not mutually exclusive since $P (A) + P (B)$ does not equal $P (A \cup B)$ . If it was $P (A \cup B) = 0.80$ only then it would have been considered mutually exclusive. Correct?

sexiboi150nc 2022-09-07

Suppose that $A$ & $B$ are mutually exclusive events. Then $P (A) = .3$ and $P (B) = .5$ . What is the probability that either $A$ or $B$ occurs? $A$ occurs but b doesn't. Both $A$ and $B$ occur.
1) Since the are mutually exclusive:
$P (A \cup B) = P (A) + P (B) = .3 + .5 = .8$
2) $A$ occurs but $B$ does not: $.3$
3) Both $A$ and $B$ occur:
Since they are mutually exclusive:
$P (A \cap B) = 0$ or the empty set
Are these correct?

luxlivinglm 2022-08-28

Which is the formal mathematical notation that the following sentence can be stated?
"Let the mutually exclusive events $A_{1}, A_{2}, \dots, A_{n}$ "

Hollywn 2022-08-21

What is the probability $P (A | A \cup B)$ generally for mutually exclusive events $A$ and $B$ ?
Suppose we have mutually exclusive events $A$ and $B$ . What would
$P (A ∣ A \cup B)$
evaluate to? would it be
$P (A ∣ A \cup B) = \frac{P (A)}{P (A \cup B)} = \frac{P (A)}{P (A) + P (B)}$
generally?

torfuqx 2022-08-20

Events $A$ and $B$ are mutually exclusive. Suppose event $A$ occurs with probability $0.19$ and event B occurs with probability $0.72$ . If $A$ does not occur, what is the probability that $B$ does not occur? Round your answer to at least two decimal places.
My answer is $0.09 / 0.81 = 0.11$
Is my answer correct?

ghettoking6q 2022-08-18

What is the difference between independent and mutually exclusive events?
Two events are mutually exclusive if they can't both happen.
Independent events are events where knowledge of the probability of one doesn't change the probability of the other.
Are these definitions correct?

Sandra Terrell 2022-08-16

Let $A, B, C,$ and $D$ be events for which and $P (A or B) = 0.6, P (A) = 0.2, P (C or D) = 0.6, and P (C) = 0.5$ . The events $A and B$ are mutually exclusive, and the events $C and D$ are independent.
(a) Find $P (B)$
This was is easy. $P (B) = P (A or B) - P (A) = .4$
(b) Find $P (D)$

sublimnes9 2022-08-15

Do mutually exclusive events simply refer to dependent events?
To add to the confusion, I also learned that mutually exclusive events can be independent event in a special case when probability is zero i.e. $P (A) = 0$ or $P (B) = 0$ .
But an event should either be independent or dependent and not both?

analianopolisca 2022-08-12

One way to check whether two events are independent is with the formula $P (A & B) = P (A) * P (B)$ . If this holds, the two events are independent (to my knowledge).
Now if $A$ and $B$ are mutually exclusive events, and $P (A) > 0$ and $P (B) > 0$ , then $P (A & B) = 0 \neq P (A) * P (B)$ , and thus the events are considered dependent. Why does this make intuitive sense?

rivasguss9 2022-08-12

Illustrate with examples, what is "mutual exclusive event" and what is "independent event".

cottencintu 2022-08-11

Events $A, B, C$ are such that $B$ and $C$ are mutually exclusive and $P (A) = 2 / 3, P (A \cup B) = 5 / 6$ and $P (B \cup C) = 4 / 5$ . If $P (B | A) = 1 / 2$ and $P (C | A) = 3 / 10$ , calculate $P (C)$ .

Landon Wolf 2022-08-09

If $P (A) = 1 / 3$ and $P (B^{∁}) = 1 / 4$ , then, can $A$ and $B$ be mutually exclusive?

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

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