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A and B are two events such that P(A)= 1/3, P(B) = ¼, P(A+B)= 1/2, than P(B/A) is equal to
- a)¼
- b)1/3
- c)1/2
- d)none
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A and B are two events such that P(A)= 1/3, P(B) = ¼, P(A+B)= 1/2...
Given: P(A) = 1/3, P(B) = x, P(A∩B) = 1/2
To find: P(B|A)
Formula: P(B|A) = P(A∩B) / P(A)
Solution:
We know that,
P(A U B) = P(A) + P(B) - P(A∩B)
Substituting the given values, we get
P(A U B) = 1/3 + x - 1/2
P(A U B) = 5/6 + x
Now, we also know that,
P(A U B) = P(A) + P(B) - P(A∩B)
Substituting the given values, we get
5/6 + x = 1/3 + x + 1/2 - 1/2
5/6 + x = 5/6 + x
Therefore, P(B|A) = P(A∩B) / P(A) = 1/2 / 1/3 = 3/2
Since probability cannot be greater than 1, the correct answer is "none of these".
Hence, option (D) is the correct answer.
To find: P(B|A)
Formula: P(B|A) = P(A∩B) / P(A)
Solution:
We know that,
P(A U B) = P(A) + P(B) - P(A∩B)
Substituting the given values, we get
P(A U B) = 1/3 + x - 1/2
P(A U B) = 5/6 + x
Now, we also know that,
P(A U B) = P(A) + P(B) - P(A∩B)
Substituting the given values, we get
5/6 + x = 1/3 + x + 1/2 - 1/2
5/6 + x = 5/6 + x
Therefore, P(B|A) = P(A∩B) / P(A) = 1/2 / 1/3 = 3/2
Since probability cannot be greater than 1, the correct answer is "none of these".
Hence, option (D) is the correct answer.
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Community Answer
A and B are two events such that P(A)= 1/3, P(B) = ¼, P(A+B)= 1/2...
Given, P(A) = 1/3, P(B), P(A ∩ B) = 1/2
We know that the conditional probability of B given A is given by:
P(B/A) = P(A ∩ B) / P(A)
Substituting the given values, we get:
P(B/A) = (1/2) / (1/3) = (1/2) x (3/1) = 3/2
But the probability of an event cannot be greater than 1. Therefore, option A is incorrect.
So, the correct answer is option D (none).
Explanation: It is not possible to calculate P(B/A) with the given information because we do not know the value of P(B ∩ A). We only know the value of P(A ∩ B) and not P(B ∩ A). Hence, none of the options given are correct.
We know that the conditional probability of B given A is given by:
P(B/A) = P(A ∩ B) / P(A)
Substituting the given values, we get:
P(B/A) = (1/2) / (1/3) = (1/2) x (3/1) = 3/2
But the probability of an event cannot be greater than 1. Therefore, option A is incorrect.
So, the correct answer is option D (none).
Explanation: It is not possible to calculate P(B/A) with the given information because we do not know the value of P(B ∩ A). We only know the value of P(A ∩ B) and not P(B ∩ A). Hence, none of the options given are correct.
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A and B are two events such that P(A)= 1/3, P(B) = ¼, P(A+B)= 1/2, than P(B/A) is equal toa)¼b)1/3c)1/2d)noneCorrect answer is option 'A'. Can you explain this answer?
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