Question

If P(A) = 1 4, P(B) = 1/3, and PAEB) = 1 2. The value of P(B/A)​

Answer 1

Answer:

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Answer 2

SOLUTION

GIVEN

P(A) = 1/4 , P(B) = 1/3 and P(AUB)= 1/2.

TO DETERMINE

The value of P(B/A)

EVALUATION

Here it is given that P(A) = 1/4 , P(B) = 1/3 and P(AUB)= 1/2.

Now

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

⇒ P(A ∩ B) = P(A) + P(B) - P(A ∪ B)

⇒ P(A ∩ B) = 1/4 + 1/3 - 1/2

⇒ P(A ∩ B) = 1/12

Thus we get

$\displaystyle \sf{P \bigg( \frac{B}{A} \bigg)}$

$\displaystyle \sf{ = \frac{P(B \cap A)}{P(A)} }$

$\displaystyle \sf{ = \frac{ \frac{1}{12} }{ \frac{1}{4} } }$

$\displaystyle \sf{ = \frac{4}{12} }$

$\displaystyle \sf{ = \frac{1}{3} }$

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