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

arenceabigns 2021-09-30 Answered
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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Expert Answer

Jayden-James Duffy
Answered 2021-10-01 Author has 17625 answers

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 \(\displaystyle{\frac{{{\frac{{{10}}}{{{13}}}}}}{{{\frac{{{3}}}{{{13}}}}}}}={10}:{3}\)

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