Pick a card from 52, odds against a king Step by Step

Step by step

The question

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

What are the odds against it being a king?

The odds against something put the outcomes against it first, then the outcomes for it.

odds against = against : for

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

Kings: 4.

kings: 1 in each suit

4 outcomes are for.

for = 4

All the others are against: 52 minus 4 is 48.

against = 52 − 4 = 48

3 Write the odds

Against, then for: 48 to 4.

odds against = 48 : 4

Careful!

Odds compare against with for.

Not with all 52.

48/52 would be a probability.

Careful: not 48 : 52 ✗

4 Simplify

Like a ratio: both 48 and 4 can be divided by 4.

odds against = (48 ÷ 4) : (4 ÷ 4)

So the odds are 12 to 1.

odds against = 12 : 1

5 Check

Let's check: for and against together are 4 plus 48, that is 52.

Every outcome is counted once.

So the answer is right!

for + against = 4 + 48 = 52 = all

Let's look back.

First: count the outcomes.

Then: count for and against.

Then: write the odds.

Then: simplify.

Last: check.

Answer