Pick a Card, Any Card
IntroductionHave you ever been playing cards and wished you could use psychic powers to draw the card you wanted? You may not be psychic, but you can still have the power of probability on your side. In this activity you'll investigate the probabilities of drawing specific types of cards from a deck. You'll discover how math can help you avoid the dreaded phrase, "Go fish!"
This activity is not appropriate for use as a science fair project. Good science fair projects have a stronger focus on controlling variables, taking accurate measurements, and analyzing data. To find a science fair project that is just right for you, browse our library of over 1,200 Science Fair Project Ideas or use the Topic Selection Wizard to get a personalized project recommendation.
BackgroundWhen you draw a card from a deck, you have a certain chance of getting a specific type of card, such as a spade or face card, or one particular card, such as the queen of hearts. Consider the game "Go Fish" with a regular card deck. The goal is to get the most four-of-a-kind sets by asking your opponent for matching cards or by drawing them from the deck. To win, you can rely on chance or you can increase your probability of getting matching cards, but how?
By understanding how chance is related to math, you can play with a winning strategy. For example, if you have three kings and one queen in your hand and it's your turn to ask for a card, which one should you ask your opponent for? You might think you should ask for a king, but it's actually better to take a queen! Why? Because you have a better chance of getting it. There are four kings and four queens in the deck, and with three kings and one queen in your hand, there's one king and three queens left. This gives you only one chance to get a king, but three chances to get a queen out of the remaining cards.
Extra: A more advanced way of showing the results of your experiment would be to make histograms, which are a type of graph to show distributions. Try making a separate histogram for each type of card you tested by graphing the number of cards drawn for each trial separately in a bar graph. When all of the bars are lined up next to each other, what does the overall shape of the distribution look like?
Extra: The probability of drawing a particular type of card also depends on the number of cards drawn each time. Try doing this activity again but draw samples of three, five or seven cards at a time. Do your chances improve as more cards are taken?
Extra: Probabilities can change your strategies for playing a card game. Can you design an experiment to show how probabilities can help you choose cards and win "Go Fish"? What about other popular card games? Can you invent your own game based on probabilities?
Observations and ResultsDid it take fewer draws to reach a certain color than it took to reach a certain suit or kind of card? Did it take even more draws to reach a specific card?
Mathematicians measure probability by counting and using some very basic math, like addition and division. For example, you can add up the number of spades in a complete deck (13) and divide this by the total number of cards in the deck (52) to get the probability of randomly drawing a spade: 13 in 52, or 25 percent. If you were investigating red cards, kings or the queen of hearts, the odds of randomly drawing one of these from a complete deck are 50 percent (26 in 52); about 7.7 percent (four in 52); or about 1.9 percent (one in 52), respectively. This is why, on average (when done over enough trials), it is easier to draw a red card than a spade, a spade than a king, and a king than the queen of hearts. As you draw cards from a deck, the odds of finding your card change. For example, if you are looking for a spade and do not get it on your first draw, there are still 13 spades in the deck but the deck now holds only 51 cards, so your odds of drawing a spade on the second draw are 13 in 51, or about 25.5 percent. This may not seem like much of an improvement, but with every draw the odds continue to increase.
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Teisha Rowland, PhD, Science Buddies
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Mathematics, probability, chance, strategy, cards
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