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If A denotes that a student reads in a school and B denotes that he plays cricket, then
- a)P(A ∩ B) = 1
- b)P(A ∪ B) = 1
- c)P(A ∩ B) = 0
- d)P(A) = P(B)
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If A denotes that a student reads in a school and B denotes that he pl...
Probability of a student reading in school and playing cricket
To solve this problem, we need to understand the definitions of probability and set theory.
Probability: Probability is the measure of the likelihood of an event occurring.
Set theory: Set theory is the branch of mathematics that deals with the study of sets, which are collections of objects.
In this problem, we are given two events:
A: A student reads in a school
B: A student plays cricket
We need to find the probability of the event A and B occurring together.
Intersection of two events
The intersection of two events is the set of elements that belong to both events.
In set theory, the intersection of two sets A and B is denoted by A ∩ B.
For example, if A = {1, 2, 3} and B = {2, 3, 4}, then A ∩ B = {2, 3}.
Probability of intersection of two events
The probability of the intersection of two events A and B is denoted by P(A ∩ B).
P(A ∩ B) represents the probability that both A and B occur.
Formula:
P(A ∩ B) = P(A) * P(B|A)
where P(B|A) represents the probability of B occurring given that A has already occurred.
If A and B are independent events, then P(B|A) = P(B), and the formula reduces to:
P(A ∩ B) = P(A) * P(B)
Solution
In this problem, we are not given any information about the relationship between A and B.
Therefore, we cannot assume that they are independent events.
Since we do not have any information about the relationship between A and B, we cannot calculate the probability of their intersection.
Therefore, the correct answer is option C: P(A ∩ B) = 0.
To solve this problem, we need to understand the definitions of probability and set theory.
Probability: Probability is the measure of the likelihood of an event occurring.
Set theory: Set theory is the branch of mathematics that deals with the study of sets, which are collections of objects.
In this problem, we are given two events:
A: A student reads in a school
B: A student plays cricket
We need to find the probability of the event A and B occurring together.
Intersection of two events
The intersection of two events is the set of elements that belong to both events.
In set theory, the intersection of two sets A and B is denoted by A ∩ B.
For example, if A = {1, 2, 3} and B = {2, 3, 4}, then A ∩ B = {2, 3}.
Probability of intersection of two events
The probability of the intersection of two events A and B is denoted by P(A ∩ B).
P(A ∩ B) represents the probability that both A and B occur.
Formula:
P(A ∩ B) = P(A) * P(B|A)
where P(B|A) represents the probability of B occurring given that A has already occurred.
If A and B are independent events, then P(B|A) = P(B), and the formula reduces to:
P(A ∩ B) = P(A) * P(B)
Solution
In this problem, we are not given any information about the relationship between A and B.
Therefore, we cannot assume that they are independent events.
Since we do not have any information about the relationship between A and B, we cannot calculate the probability of their intersection.
Therefore, the correct answer is option C: P(A ∩ B) = 0.
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Community Answer
If A denotes that a student reads in a school and B denotes that he pl...
This mathematical expression indicate the no. of common student who reads as well as play
therefore, there is no common student as per the question
hence, it equals to zero
therefore, there is no common student as per the question
hence, it equals to zero
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If A denotes that a student reads in a school and B denotes that he plays cricket, thena)P(A ∩ B) = 1b)P(A ∪ B) = 1c)P(A ∩ B) = 0d)P(A) = P(B)Correct answer is option 'C'. Can you explain this answer?
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If A denotes that a student reads in a school and B denotes that he plays cricket, thena)P(A ∩ B) = 1b)P(A ∪ B) = 1c)P(A ∩ B) = 0d)P(A) = P(B)Correct answer is option 'C'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If A denotes that a student reads in a school and B denotes that he plays cricket, thena)P(A ∩ B) = 1b)P(A ∪ B) = 1c)P(A ∩ B) = 0d)P(A) = P(B)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A denotes that a student reads in a school and B denotes that he plays cricket, thena)P(A ∩ B) = 1b)P(A ∪ B) = 1c)P(A ∩ B) = 0d)P(A) = P(B)Correct answer is option 'C'. Can you explain this answer?.
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If A denotes that a student reads in a school and B denotes that he plays cricket, thena)P(A ∩ B) = 1b)P(A ∪ B) = 1c)P(A ∩ B) = 0d)P(A) = P(B)Correct answer is option 'C'. Can you explain this answer?, a detailed solution for If A denotes that a student reads in a school and B denotes that he plays cricket, thena)P(A ∩ B) = 1b)P(A ∪ B) = 1c)P(A ∩ B) = 0d)P(A) = P(B)Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of If A denotes that a student reads in a school and B denotes that he plays cricket, thena)P(A ∩ B) = 1b)P(A ∪ B) = 1c)P(A ∩ B) = 0d)P(A) = P(B)Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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