Step 1

Total number of cards \(\displaystyle={52}\)

One card is drawn randomly.

Step 2

P(face card):-

Number of favourable outcomes \(\displaystyle={12}\) (Face card)

P( face card ) \(= \frac{12}{52} =\frac{3}{13}\)

P(not face card) \(\displaystyle={1}-{\left({\frac{{{3}}}{{{13}}}}\right)}\)

\(\displaystyle={\frac{{{10}}}{{{13}}}}\)

To convert probability to odds divide the probability by 1 - that probability

Odds in favor of drawing a face card are \(\displaystyle{\frac{{{\frac{{{3}}}{{{13}}}}}}{{{\frac{{{10}}}{{{13}}}}}}}={3}:{10}\)

Odds in favor of not drawing a face card are \(\displaystyle{\frac{{{\frac{{{10}}}{{{13}}}}}}{{{\frac{{{3}}}{{{13}}}}}}}={10}:{3}\)