Browse Questions

Let A,B,C be three equally likely and collectively exhaustive events. If the odds 8 : 3 against A, 5:2 against B then the odds against C are

$\begin {array} {1 1} (A)\;20:17 & \quad (B)\;50:31 \\ (C)\;3:34 & \quad (D)\;77:34 \end {array}$

$P(A)=\large\frac{3}{11}$
$P(B)=\large\frac{2}{7}$
$P(C)=1-(P(A)+P(B))$
$=1-\bigg( \large\frac{3}{11}+\large\frac{2}{7} \bigg)$
$= \large\frac{34}{77}$
Odds against C are 43 : 34