Pick a card from 52, odds for a face card Step by Step

Step by step

The question

Question: A card is picked from a deck of 52 cards.

What are the odds for it being a face card?

The odds for something compare the outcomes for it, with the outcomes against it.

odds for = for : against

For: the outcomes we want.

Against: all the others.

for = we want, against = the others

1 Count the outcomes

A deck has 4 suits of 13 cards: 52 cards.

4 suits × 13 cards = 52

So there are 52 outcomes in all, each just as likely.

all = 52

2 Count for and against

Face cards: 12.

face cards: J, Q, K in 4 suits

12 outcomes are for.

for = 12

All the others are against: 52 minus 12 is 40.

against = 52 − 12 = 40

3 Write the odds

For, then against: 12 to 40.

odds for = 12 : 40

Careful!

Odds compare for with against.

Not with all 52.

12/52 would be a probability.

Careful: not 12 : 52 ✗

4 Simplify

Like a ratio: both 12 and 40 can be divided by 4.

odds for = (12 ÷ 4) : (40 ÷ 4)

So the odds are 3 to 10.

odds for = 3 : 10

5 Check

Let's check: for and against together are 12 plus 40, that is 52.

Every outcome is counted once.

So the answer is right!

for + against = 12 + 40 = 52 = all

Let's look back.

First: count the outcomes.

Then: count for and against.

Then: write the odds.

Then: simplify.

Last: check.

Answer