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Let E and F be two independent events. The probability that exactly one of them occurs is 
and the probability of none of them occurring is 
. If P(T) denotes the probability of occurrence of the event T, then (2011)
and the probability of none of them occurring is . If P(T) denotes the probability of occurrence of the event T, then (2011)- a)
- b)
- c)
- d)
Correct answer is option 'A,D'. Can you explain this answer?
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Let E and F be two independent events. The probability that exactly on...
Q E and F are independent events
∴ P( E ∩F) = P(E). P(F) ...(1)
Given that 
⇒ P(E) ( 1 – P (F)) + (1 – P (E)) P (F) = 
⇒ P (E) – P (E) P (F) + P (F) – P(E) P (F) =
⇒ P (E) + P (F) – 2 P(E). P(F) = ...(2)
...(2)and 
⇒ 1 – P(E) – P(F) + P(E) P(F) = 
...(3)
...(3)Adding equation (2) and (3) we get
1 – P(E) P(F) = 
or P(E) P(F) = 
...(4)
or P(E) P(F) = ...(4)Using the result in equation (2) we get
...(5)Solving (4) and (5) we get
P(E) = 
and P(F) = 
or P(E) = and P(F) =
and P(F) = or P(E) = and P(F) = ∴ (a) and (d) are the correct options.
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Let E and F be two independent events. The probability that exactly one of them occurs is and the probability of none of them occurring is . If P(T) denotes the probability of occurrence of the event T, then (2011)a)b)c)d)Correct answer is option 'A,D'. Can you explain this answer?
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Let E and F be two independent events. The probability that exactly one of them occurs is and the probability of none of them occurring is . If P(T) denotes the probability of occurrence of the event T, then (2011)a)b)c)d)Correct answer is option 'A,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 E and F be two independent events. The probability that exactly one of them occurs is and the probability of none of them occurring is . If P(T) denotes the probability of occurrence of the event T, then (2011)a)b)c)d)Correct answer is option 'A,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 E and F be two independent events. The probability that exactly one of them occurs is and the probability of none of them occurring is . If P(T) denotes the probability of occurrence of the event T, then (2011)a)b)c)d)Correct answer is option 'A,D'. Can you explain this answer?.
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Let E and F be two independent events. The probability that exactly one of them occurs is and the probability of none of them occurring is . If P(T) denotes the probability of occurrence of the event T, then (2011)a)b)c)d)Correct answer is option 'A,D'. Can you explain this answer?, a detailed solution for Let E and F be two independent events. The probability that exactly one of them occurs is and the probability of none of them occurring is . If P(T) denotes the probability of occurrence of the event T, then (2011)a)b)c)d)Correct answer is option 'A,D'. Can you explain this answer? has been provided alongside types of Let E and F be two independent events. The probability that exactly one of them occurs is and the probability of none of them occurring is . If P(T) denotes the probability of occurrence of the event T, then (2011)a)b)c)d)Correct answer is option 'A,D'. Can you explain this answer? theory, EduRev gives you an
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