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A and B are two independent events. P( A and B) = 1/6 and the probability that neither of them occur is 1/3 . Find the probability occurrence of A?
- a)1/4
- b)1/3
- c)1/5
- d)1/8
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A and B are two independent events. P( A and B) = 1/6 and the probabil...
Let P(A) = X and P(B) = Y;
So, P(A’) = 1 - X and P(B’) = 1 - Y
P(A and B) = P(A) x P(B) = XY = 1/6
Probability that neither of them occurs = P(A’) x P(B’) = (1 - X) x (1 - Y) = 1/3
Solving the resulting quadratic equation, we get X = 1/3 or 1/2 that is the probability of occurrence of A
So, P(A’) = 1 - X and P(B’) = 1 - Y
P(A and B) = P(A) x P(B) = XY = 1/6
Probability that neither of them occurs = P(A’) x P(B’) = (1 - X) x (1 - Y) = 1/3
Solving the resulting quadratic equation, we get X = 1/3 or 1/2 that is the probability of occurrence of A
Most Upvoted Answer
A and B are two independent events. P( A and B) = 1/6 and the probabil...
Given Information:
- P(A and B) = 1/6
- P(neither A nor B) = 1/3
Calculating P(A):
Let's denote P(A) as x.
Formula:
P(A or B) = P(A) + P(B) - P(A and B)
Given:
P(neither A nor B) = 1/3
Formula:
P(neither A nor B) = 1 - P(A or B)
Substitute the values:
1/3 = 1 - [P(A) + P(B) - 1/6]
1/3 = 1 - [x + P(B) - 1/6]
Given:
P(A and B) = 1/6
Substitute the values:
1/3 = 1 - [x + 1/6 - 1/6]
1/3 = 1 - x
Solve for x:
x = 1 - 1/3
x = 2/3
Therefore, the probability of the occurrence of A is 2/3, which is equivalent to 1/3. Hence, the correct answer is option B) 1/3.
- P(A and B) = 1/6
- P(neither A nor B) = 1/3
Calculating P(A):
Let's denote P(A) as x.
Formula:
P(A or B) = P(A) + P(B) - P(A and B)
Given:
P(neither A nor B) = 1/3
Formula:
P(neither A nor B) = 1 - P(A or B)
Substitute the values:
1/3 = 1 - [P(A) + P(B) - 1/6]
1/3 = 1 - [x + P(B) - 1/6]
Given:
P(A and B) = 1/6
Substitute the values:
1/3 = 1 - [x + 1/6 - 1/6]
1/3 = 1 - x
Solve for x:
x = 1 - 1/3
x = 2/3
Therefore, the probability of the occurrence of A is 2/3, which is equivalent to 1/3. Hence, the correct answer is option B) 1/3.
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A and B are two independent events. P( A and B) = 1/6 and the probability that neither of them occur is 1/3 . Find the probability occurrence of A?a)1/4b)1/3c)1/5d)1/8Correct answer is option 'B'. 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 A and B are two independent events. P( A and B) = 1/6 and the probability that neither of them occur is 1/3 . Find the probability occurrence of A?a)1/4b)1/3c)1/5d)1/8Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A and B are two independent events. P( A and B) = 1/6 and the probability that neither of them occur is 1/3 . Find the probability occurrence of A?a)1/4b)1/3c)1/5d)1/8Correct answer is option 'B'. Can you explain this answer?.
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