There are four suits per deck, each of which consists of the following cards: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, and King. What is the probability of drawing a 5 from a deck of cards?

To determine probability, divide the number of desired outcomes by the number of total possible outcomes, and then convert the fraction into a percent.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

What we're dealing with here is the concept of probability, or how likely it is that an event will happen. To measure the probability of an event, we use a simple formula. We take the number of ways that an event can happen (i.e. the number of desired outcomes) and divide that by the total number of possible outcomes.

Let's start with an easy example. If we flip a coin and call heads, our desired outcome becomes heads rather than tails. We have one shot at heads, but there are two possible outcomes. So we divide 1 by 2, and we get ½ or 50%. We have a 50-50 shot of the coin actually showing heads when it lands.

Let's try another probability problem. Let's say we roll a dice and want want to roll a two. We have one shot to see a two, but now we have six possible outcomes because the dice has six sides. We divide 1 by 6 for 1/6 or a 16.67% chance that we will roll a two.

Now let's look at this card problem. There are 52 cards in a deck, and we might draw any one of them, so we have 52 possible outcomes. What we want, though, is a five. Since there are four suits in a deck, there are four five-cards, one for each suit. So our number of desired outcomes is four. We would be happy to draw any of the five-cards. Now we divide our number of desired outcomes (four) by the number of total possible outcomes (52), and we have 4/52. We can simplify this fraction to 1/13 and turn it into the percentage 7.69%. For any draw we make, we have a 7.69% chance of drawing a five-card.

Last Updated by eNotes Editorial on
Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial