JEE Exam > JEE Questions > If P(B)=(3/4), P(A∩B∩C) = (1/3) and P...
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If P(B)=(3/4), P(A∩B∩C̅) = (1/3) and P(A̅∩B∩C̅) = 1/3, then P(B∩C) is
- a)1/12
- b)1/6
- c)1/15
- d)1/9
Correct answer is option 'A'. Can you explain this answer?
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If P(B)=(3/4), P(A∩B∩C) = (1/3) and P(A∩B∩C) = 1/3, th...
Given Information:
P(B) = 3/4
P(A ∩ B ∩ C) = 1/3
P(A ∩ B ∩ C) = 1/3
Calculating P(B ∩ C):
To find P(B ∩ C), we can use the formula:
P(A ∩ B ∩ C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C)
Substitute the given values into the formula:
1/3 = P(A) + 3/4 + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) + 1/3
Since P(A) + P(B) + P(C) = 1 (total probability),
1/3 = 1 - P(A ∩ B) - P(A ∩ C) - P(B ∩ C)
Given that P(A ∩ B ∩ C) = 1/3,
P(B ∩ C) = 1 - 1/3 - 1/3 = 1/3
Therefore, P(B ∩ C) = 1/3 which is equivalent to 1/12. Hence, the correct answer is option 'A'.
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If P(B)=(3/4), P(A∩B∩C) = (1/3) and P(A∩B∩C) = 1/3, then P(B∩C) isa)1/12b)1/6c)1/15d)1/9Correct answer is option 'A'. Can you explain this answer?
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