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Let A and B be two events such that the probability that exactly one of them occurs is 2/5 and the probability that A or B occurs is 1/2, then the probability that both of them occur together is
  • a)
    0.01
  • b)
    0.20
  • c)
    0.02
  • d)
    0.10
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Let A and B be two events such that the probability that exactly one o...
To find the probability that both events A and B occur together, we can use the formula:

P(A and B) = P(A) + P(B) - P(A or B)

Given:
P(A or B) = 1/2
P(exactly one of A or B) = 2/5

Let's solve step by step:

1. Probability of exactly one of A or B occurring:
P(exactly one of A or B) = P(A) + P(B) - 2P(A and B)
2/5 = P(A) + P(B) - 2P(A and B) ...(1)

2. Probability of A or B occurring:
P(A or B) = P(A) + P(B) - P(A and B)
1/2 = P(A) + P(B) - P(A and B) ...(2)

3. Subtracting equation (2) from equation (1) to eliminate P(A) + P(B):
2/5 - 1/2 = -P(A and B) + P(A and B)
(4/10) - (5/10) = -P(A and B)
-1/10 = -P(A and B)
P(A and B) = 1/10

Thus, the probability that both events A and B occur together is 1/10, which is equivalent to 0.10. Therefore, the correct answer is option D.
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Let A and B be two events such that the probability that exactly one of them occurs is 2/5 and the probability that A or B occurs is 1/2, then the probability that both of them occur together isa)0.01b)0.20c)0.02d)0.10Correct answer is option 'D'. Can you explain this answer?
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Let A and B be two events such that the probability that exactly one of them occurs is 2/5 and the probability that A or B occurs is 1/2, then the probability that both of them occur together isa)0.01b)0.20c)0.02d)0.10Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let A and B be two events such that the probability that exactly one of them occurs is 2/5 and the probability that A or B occurs is 1/2, then the probability that both of them occur together isa)0.01b)0.20c)0.02d)0.10Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let A and B be two events such that the probability that exactly one of them occurs is 2/5 and the probability that A or B occurs is 1/2, then the probability that both of them occur together isa)0.01b)0.20c)0.02d)0.10Correct answer is option 'D'. Can you explain this answer?.
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