**Question **: Given two events . If odds against A are as 2:1 and those in favour of AUB are as 3:1, then

(A) 1/2 ≤ P(B) ≤ 3/4

(B) 5/12 ≤ P(B) ≤ 3/4

(C) 1/4 ≤ P(B) ≤ 3/5

(D) none of these

**Answer **: option (B)

**Solution **:

P(A) = 1/3, P(AUB) = 3/4

now, P\left( A\cup B\right) =P\left( A\right) +P\left( B\right) -P\left( A\cap B\right) \leq P\left( A\right) +P\left( B\right) \Rightarrow \dfrac{3}{4}\leq \dfrac{1}{3}+P\left( B\right) \Rightarrow \dfrac{5}{12}\leq P\left( B\right)

Again we have, B ⊆ A U B

therefore, P\left( B\right) \leq P\left( A\cup B\right) =\dfrac{3}{4}

hence, 5/12 ≤ P(B) ≤ 3/4