Question

One card is randomly selected from a deck of cards. Find the odds against drawing a three​

Answer 1

The answer is 12:1

note: this is often read as "12 to 1"

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Explanation

We have exactly four card that are labeled "3" and 52 cards total. So there are 52-4 = 48 cards that are not labeled "3".

From here you write the ratio 48:4 to indicate the odds against drawing a 3. There are 48 ways to lose, 4 ways to win. You list the number of ways to lose first when it comes to "odds against" type of problems.

Next step is to reduce the ratio 48:4 to get 12:1, note how I divided both parts by the GCF 4

48/4 = 12

4/4 = 1

So thats how 48:4 reduces to 12:1

If you focus on one suit, say the spades, then we have 12 cards that arent a 3 of spades while exactly one card is a 3 of spades. This is one way to see why 12:1 is the answer. If you were saying this out loud to a friend, then you might say something like "the odds against drawing a three are 12 to 1".