Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > If P and Q are two random events, then the fo...
Start Learning for Free
If P and Q are two random events, then the following is TRUE:
- a)Independence of P and Q implies that probability (P ∩ Q) = 0
- b)Probability (P ∪ Q) ≥ Probability (P) + Probability (Q)
- c)If P and Q are mutually exclusive, then they must be independent
- d)Probability (P ∩ Q) ≤ Probability (P)
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
If P and Q are two random events, then the following is TRUE:a)Indepen...
here i check option---> i let P = probability, P and Q is replaced by A and B.
A) it is saying independent means P(A ^ B) = P(A)* P(B) so option A is false
B) P(AÜ B) = P(A) + P(B) - P(A ^ B)
hence P(AÜB) >= P(A) + P(B) its false option B is false
C) if A and B is mutually exclusive means P(A ^ B) = 0 then its independent ........its false there is no relation independent and mutually exclusive
D) P(A ^ B) <= P(A)
A) it is saying independent means P(A ^ B) = P(A)* P(B) so option A is false
B) P(AÜ B) = P(A) + P(B) - P(A ^ B)
hence P(AÜB) >= P(A) + P(B) its false option B is false
C) if A and B is mutually exclusive means P(A ^ B) = 0 then its independent ........its false there is no relation independent and mutually exclusive
D) P(A ^ B) <= P(A)
its true
hence option D is correct
Most Upvoted Answer
If P and Q are two random events, then the following is TRUE:a)Indepen...
here i check option---> i let P = probability, P and Q is replaced by A and B.
A) it is saying independent means P(A ^ B) = P(A)* P(B) so option A is false
B) P(AÜ B) = P(A) + P(B) - P(A ^ B)
hence P(AÜB) >= P(A) + P(B) its false option B is false
C) if A and B is mutually exclusive means P(A ^ B) = 0 then its independent ........its false there is no relation independent and mutually exclusive
D) P(A ^ B) <= P(A)
A) it is saying independent means P(A ^ B) = P(A)* P(B) so option A is false
B) P(AÜ B) = P(A) + P(B) - P(A ^ B)
hence P(AÜB) >= P(A) + P(B) its false option B is false
C) if A and B is mutually exclusive means P(A ^ B) = 0 then its independent ........its false there is no relation independent and mutually exclusive
D) P(A ^ B) <= P(A)
its true
hence option D is correct
Free Test
FREE
| Start Free Test |
Community Answer
If P and Q are two random events, then the following is TRUE:a)Indepen...
Probability (P ∩ Q) ≤ Probability (P)
To understand why option D is the correct answer, let's break down the statement and discuss each part separately.
Probability (P ∩ Q) represents the probability of both events P and Q occurring simultaneously. This can also be written as the joint probability of P and Q.
Probability (P) represents the probability of event P occurring.
The statement in option D states that Probability (P ∩ Q) ≤ Probability (P).
To understand why this statement is true, consider the following:
1. If events P and Q are independent, then the occurrence of one event does not affect the probability of the other event occurring. In this case, the joint probability of P and Q would be equal to the product of the probabilities of each event occurring independently.
For example, if the probability of event P occurring is 0.5 and the probability of event Q occurring is 0.3, then the joint probability of P and Q occurring would be 0.5 * 0.3 = 0.15.
In this case, the joint probability (0.15) is less than or equal to the probability of event P occurring (0.5), which confirms the statement in option D.
2. If events P and Q are dependent, then the occurrence of one event affects the probability of the other event occurring. In this case, the joint probability of P and Q would not necessarily be less than or equal to the probability of event P occurring.
For example, if the probability of event P occurring is 0.5 and the probability of event Q occurring is 0.7, and there is a strong dependence between the two events, the joint probability of P and Q occurring could be greater than 0.5.
In this case, the joint probability would not satisfy the inequality in option D, indicating that the events are dependent.
Therefore, the statement in option D holds true because it covers both scenarios of independent and dependent events. If events P and Q are independent, the joint probability would be less than or equal to the probability of event P occurring. If events P and Q are dependent, the joint probability could be greater than the probability of event P occurring, thus not satisfying the inequality.
To understand why option D is the correct answer, let's break down the statement and discuss each part separately.
Probability (P ∩ Q) represents the probability of both events P and Q occurring simultaneously. This can also be written as the joint probability of P and Q.
Probability (P) represents the probability of event P occurring.
The statement in option D states that Probability (P ∩ Q) ≤ Probability (P).
To understand why this statement is true, consider the following:
1. If events P and Q are independent, then the occurrence of one event does not affect the probability of the other event occurring. In this case, the joint probability of P and Q would be equal to the product of the probabilities of each event occurring independently.
For example, if the probability of event P occurring is 0.5 and the probability of event Q occurring is 0.3, then the joint probability of P and Q occurring would be 0.5 * 0.3 = 0.15.
In this case, the joint probability (0.15) is less than or equal to the probability of event P occurring (0.5), which confirms the statement in option D.
2. If events P and Q are dependent, then the occurrence of one event affects the probability of the other event occurring. In this case, the joint probability of P and Q would not necessarily be less than or equal to the probability of event P occurring.
For example, if the probability of event P occurring is 0.5 and the probability of event Q occurring is 0.7, and there is a strong dependence between the two events, the joint probability of P and Q occurring could be greater than 0.5.
In this case, the joint probability would not satisfy the inequality in option D, indicating that the events are dependent.
Therefore, the statement in option D holds true because it covers both scenarios of independent and dependent events. If events P and Q are independent, the joint probability would be less than or equal to the probability of event P occurring. If events P and Q are dependent, the joint probability could be greater than the probability of event P occurring, thus not satisfying the inequality.
Attention Computer Science Engineering (CSE) Students!
To make sure you are not studying endlessly, EduRev has designed Computer Science Engineering (CSE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Computer Science Engineering (CSE).
|
Explore Courses for Computer Science Engineering (CSE) exam
|
|
Similar Computer Science Engineering (CSE) Doubts
Top Courses for Computer Science Engineering (CSE)View all
If P and Q are two random events, then the following is TRUE:a)Independence of P and Q implies that probability (P ∩ Q) = 0b)Probability (P ∪ Q) ≥ Probability (P) + Probability (Q)c)If P and Q are mutually exclusive, then they must be independentd)Probability (P ∩ Q) ≤ Probability (P)Correct answer is option 'D'. Can you explain this answer?
Question Description
If P and Q are two random events, then the following is TRUE:a)Independence of P and Q implies that probability (P ∩ Q) = 0b)Probability (P ∪ Q) ≥ Probability (P) + Probability (Q)c)If P and Q are mutually exclusive, then they must be independentd)Probability (P ∩ Q) ≤ Probability (P)Correct answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about If P and Q are two random events, then the following is TRUE:a)Independence of P and Q implies that probability (P ∩ Q) = 0b)Probability (P ∪ Q) ≥ Probability (P) + Probability (Q)c)If P and Q are mutually exclusive, then they must be independentd)Probability (P ∩ Q) ≤ Probability (P)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If P and Q are two random events, then the following is TRUE:a)Independence of P and Q implies that probability (P ∩ Q) = 0b)Probability (P ∪ Q) ≥ Probability (P) + Probability (Q)c)If P and Q are mutually exclusive, then they must be independentd)Probability (P ∩ Q) ≤ Probability (P)Correct answer is option 'D'. Can you explain this answer?.
If P and Q are two random events, then the following is TRUE:a)Independence of P and Q implies that probability (P ∩ Q) = 0b)Probability (P ∪ Q) ≥ Probability (P) + Probability (Q)c)If P and Q are mutually exclusive, then they must be independentd)Probability (P ∩ Q) ≤ Probability (P)Correct answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about If P and Q are two random events, then the following is TRUE:a)Independence of P and Q implies that probability (P ∩ Q) = 0b)Probability (P ∪ Q) ≥ Probability (P) + Probability (Q)c)If P and Q are mutually exclusive, then they must be independentd)Probability (P ∩ Q) ≤ Probability (P)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If P and Q are two random events, then the following is TRUE:a)Independence of P and Q implies that probability (P ∩ Q) = 0b)Probability (P ∪ Q) ≥ Probability (P) + Probability (Q)c)If P and Q are mutually exclusive, then they must be independentd)Probability (P ∩ Q) ≤ Probability (P)Correct answer is option 'D'. Can you explain this answer?.
Solutions for If P and Q are two random events, then the following is TRUE:a)Independence of P and Q implies that probability (P ∩ Q) = 0b)Probability (P ∪ Q) ≥ Probability (P) + Probability (Q)c)If P and Q are mutually exclusive, then they must be independentd)Probability (P ∩ Q) ≤ Probability (P)Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Computer Science Engineering (CSE).
Download more important topics, notes, lectures and mock test series for Computer Science Engineering (CSE) Exam by signing up for free.
Here you can find the meaning of If P and Q are two random events, then the following is TRUE:a)Independence of P and Q implies that probability (P ∩ Q) = 0b)Probability (P ∪ Q) ≥ Probability (P) + Probability (Q)c)If P and Q are mutually exclusive, then they must be independentd)Probability (P ∩ Q) ≤ Probability (P)Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If P and Q are two random events, then the following is TRUE:a)Independence of P and Q implies that probability (P ∩ Q) = 0b)Probability (P ∪ Q) ≥ Probability (P) + Probability (Q)c)If P and Q are mutually exclusive, then they must be independentd)Probability (P ∩ Q) ≤ Probability (P)Correct answer is option 'D'. Can you explain this answer?, a detailed solution for If P and Q are two random events, then the following is TRUE:a)Independence of P and Q implies that probability (P ∩ Q) = 0b)Probability (P ∪ Q) ≥ Probability (P) + Probability (Q)c)If P and Q are mutually exclusive, then they must be independentd)Probability (P ∩ Q) ≤ Probability (P)Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of If P and Q are two random events, then the following is TRUE:a)Independence of P and Q implies that probability (P ∩ Q) = 0b)Probability (P ∪ Q) ≥ Probability (P) + Probability (Q)c)If P and Q are mutually exclusive, then they must be independentd)Probability (P ∩ Q) ≤ Probability (P)Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If P and Q are two random events, then the following is TRUE:a)Independence of P and Q implies that probability (P ∩ Q) = 0b)Probability (P ∪ Q) ≥ Probability (P) + Probability (Q)c)If P and Q are mutually exclusive, then they must be independentd)Probability (P ∩ Q) ≤ Probability (P)Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Computer Science Engineering (CSE) tests.
|
|
Explore Courses for Computer Science Engineering (CSE) exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup