Odds in favour of an event A are 2 to 1 and odds in favour of A ∪ B are 3 to 1. Consistent with this information the smallest and largest values for the probability of event B are given by
Answer & explanation
Correct answer: option 3
We have,
$P(A) =\frac{2}{3}, P(A ∪ B) =\frac{3}{4}$
$∴ P(A ∪ B) = P(A) +P(B) -P( A ∩ B)$
$⇒ \frac{3}{4}=\frac{2}{3} + P(B) -P(A ∩ B)$
$⇒ P(A ∩ B)= P(B) -\frac{1}{12}$
Now,
$0 ≤ P (A ∩ B) ≤ P(A)$
$⇒ 0 ≤P(B)-\frac{1}{12} ≤ P(A)⇒ \frac{1}{12} ≤ P(B) ≤ \frac{3}{4}$