Pick a card from 52, odds for a heart 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 heart?

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

Hearts: 13.

hearts: 1 suit of 13

13 outcomes are for.

for = 13

All the others are against: 52 minus 13 is 39.

against = 52 − 13 = 39

3 Write the odds

For, then against: 13 to 39.

odds for = 13 : 39

Careful!

Odds compare for with against.

Not with all 52.

13/52 would be a probability.

Careful: not 13 : 52 ✗

4 Simplify

Like a ratio: both 13 and 39 can be divided by 13.

odds for = (13 ÷ 13) : (39 ÷ 13)

So the odds are 1 to 3.

odds for = 1 : 3

5 Check

Let's check: for and against together are 13 plus 39, that is 52.

Every outcome is counted once.

So the answer is right!

for + against = 13 + 39 = 52 = all

Let's look back.

First: count the outcomes.

Then: count for and against.

Then: write the odds.

Then: simplify.

Last: check.

Answer