CA Foundation Exam > CA Foundation Questions > Let A and B be the events with P(A)= 1/3, P(B...
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Let A and B be the events with P(A)= 1/3, P(B) = ¼ and P(AB)= 1/12 then P(A/B) is equal to
- a)1/3
- b)¼
- c)¾
- d)2/3
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Let A and B be the events with P(A)= 1/3, P(B) = and P(AB)= 1/12 then...
To find the conditional probability P(A/B), we can use the formula:
P(A/B) = P(AB) / P(B)
Given:
P(A) = 1/3
P(B) = ?
P(AB) = 1/12
We need to find the value of P(B).
Step 1: Finding P(B)
To find P(B), we can use the formula:
P(AB) = P(A) * P(B)
Given:
P(AB) = 1/12
P(A) = 1/3
Substituting the given values into the formula:
1/12 = (1/3) * P(B)
Simplifying the equation:
P(B) = (1/12) / (1/3)
P(B) = (1/12) * (3/1)
P(B) = 3/12
P(B) = 1/4
Therefore, P(B) = 1/4.
Step 2: Finding P(A/B)
Now that we have the values of P(A) and P(B), we can substitute them into the formula for conditional probability:
P(A/B) = P(AB) / P(B)
Given:
P(AB) = 1/12
P(B) = 1/4
Substituting the given values into the formula:
P(A/B) = (1/12) / (1/4)
To divide by a fraction, we can multiply by its reciprocal:
P(A/B) = (1/12) * (4/1)
Simplifying the equation:
P(A/B) = (1/12) * (4/1)
P(A/B) = 4/12
P(A/B) = 1/3
Therefore, P(A/B) is equal to 1/3.
Hence, the correct answer is option 'A' - 1/3.
P(A/B) = P(AB) / P(B)
Given:
P(A) = 1/3
P(B) = ?
P(AB) = 1/12
We need to find the value of P(B).
Step 1: Finding P(B)
To find P(B), we can use the formula:
P(AB) = P(A) * P(B)
Given:
P(AB) = 1/12
P(A) = 1/3
Substituting the given values into the formula:
1/12 = (1/3) * P(B)
Simplifying the equation:
P(B) = (1/12) / (1/3)
P(B) = (1/12) * (3/1)
P(B) = 3/12
P(B) = 1/4
Therefore, P(B) = 1/4.
Step 2: Finding P(A/B)
Now that we have the values of P(A) and P(B), we can substitute them into the formula for conditional probability:
P(A/B) = P(AB) / P(B)
Given:
P(AB) = 1/12
P(B) = 1/4
Substituting the given values into the formula:
P(A/B) = (1/12) / (1/4)
To divide by a fraction, we can multiply by its reciprocal:
P(A/B) = (1/12) * (4/1)
Simplifying the equation:
P(A/B) = (1/12) * (4/1)
P(A/B) = 4/12
P(A/B) = 1/3
Therefore, P(A/B) is equal to 1/3.
Hence, the correct answer is option 'A' - 1/3.
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