Odds with Probability

Question

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

Write all answers as simplified fractions (not mixed numbers):

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

Answer 1

Face cards are J, Q and K and there are 4 of each in a standard 52 card deck, 12 total.

So probability of drawing a face card is 12/52 = 3/13

Probability of drawing a face card + Probability of NOT drawing a face card = 1

3/13 + probability of drawing a face card = 1

probability of not drawing a face card = 10/13

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

Odds in favor of drawing a face card are 3/13 / 10 /13 = 3:10

Odds in favor of not drawing a face card are 10/13 / 3/13 = 10:3