Question

One of the two events, A and B must occur. If $P\left(A\right)=\frac{2}{3}P\left(B\right),$ the odds in favour of $B$ are

• A. $1:3$
• B. $2:1$
• C. $2:3$
• D. $3:2$

Answer 1

The correct option is D $3:2$

One of the two events $A$ and $B$ must occur, So: $P\left(A\right)+P\left(B\right)=1$
$\frac{2}{3}P\left(B\right)+P\left(B\right)=1$
$P\left(B\right)=\frac{3}{5}$
Odds in favour of $B=3:2$