Question

Sol. [Key Concept: Mis-counted pack of cards: conditional probability.]

Odds against missing card being spade

$$\begin{matrix} & \ = \frac{P(\text{~}\text{missing card is not spade \textbackslash\& 2cards drawn are spades}\text{~})}{P(\text{~}\text{missing card is spade \textbackslash\& 2cards drawn are spades}\text{~})} \\ & \ = \frac{\frac{3}{4} \times \frac{13C_{2}}{51C_{2}}}{\frac{1}{4} \times \frac{12C_{2}}{51C_{2}}} \\ & \ = \frac{3 \times 13 \times 12}{12 \times 11} = \frac{39}{11} \end{matrix}$$