# A card is drawn randomly from a standard 52-card deck. Find the following: Writ

A card is drawn randomly from a standard 52-card deck. Find the following: Write all answers as simplified fractions. Probability the card drawn is a face card. Probability the card drawn is not a face card. Odds in favor of drawing a face card. Odds against drawing a face card.

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Jayden-James Duffy

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 $$\displaystyle{\frac{{{\frac{{{10}}}{{{13}}}}}}{{{\frac{{{3}}}{{{13}}}}}}}={10}:{3}$$