How to Calculate Theoretical Probability
In mathematics, theoretical probability is the number of ways an event can occur divided by the total possible outcomes of the event. This may sound complicated as an abstract concept, but theoretical probability can be clarified through the use of visual examples.
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Instructions
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Coin Flip
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Flip the coin. The flipping of the coin is the event. Notice that there is only one way to flip a coin. Therefore, the number of ways the event can occur is 1. The theoretical probability formula is "(number of ways the event can occur) / (number of possible outcomes)". So the equation so far is "1 / (number of possible outcomes)".
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Notice that flipping the coin can only result in two outcomes: heads or tails. Now the equation is 1/2. Another way of saying this is that you have a 1 in 2 chance of getting heads by flipping the coin once. This makes the theoretical probability of getting heads 1/2, or 0.5. You could also say that you have a 50% chance of the flip resulting in heads.
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Notice that during the times you don't land heads, you get tails. Therefore, the theoretical probability is the same for tails.
Dice Roll
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Examine one of the dice, which is called a die. An ordinary die has six sides, each with a different number on it.
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Roll the die. Notice that no matter how you toss it, it always results in one side facing up. This means that there is only one way the event -- the tossing -- can occur. Your equation so far is 1 / number of possible outcomes.
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Notice that while one side of the die always faces up, the number on that side can change. There are six different numbers on the die. Therefore, there are six different outcomes to the event. You have a 1 in 6 chance of the side facing up to have a 2 on it. Another way of saying this is that the probability of rolling a 2 is 1/6. Divide 1 into 6 to get approximately 0.17. Multiple 0.17 by 100 to get a 17% chance of rolling a 2.
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Notice that like the coin flip, each side of the die has the same potential to land face up after you roll it. This makes the probability of rolling a 3, a 4, a 5, a 6, or a 1 equal to rolling a 2.
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Consider the number of possible outcomes that can occur when a pair of a dice is rolled, rather than a single die. For example, you can have a 1 and 2 land face up. But you don't always get a 1 and 2 when you roll a pair of dice.
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Write down all of the number combinations that can occur by rolling two 6-sided dice. Your chances of rolling a 1 and a 2 are 1 in 36, or 1/36, or approximately 0.028. Multiple 0.028 by 100 to get a 2.8% chance. Each of the combinations has the same probability of occuring, so the theoretical probability is always 1/36 in this case.
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Tips & Warnings
Practice the calculation by applying it to different objects and actions. For example, you could spin a colored spinner from a board game or grab random handfuls of different colored marbles. The formula doesn't change.
Keep in mind that theoretical probability is different from experimental probability. Experimental probability is found by recording each coin flip or dice toss and seeing which outcomes actually occur, rather than estimating them. For example, in theoretical probability, you have a 50% chance of getting heads when flipping a coin. But if you were to flip a coin 20 times and get heads from only 8 of those times, the probability of landing heads specific to your experiment is 2/5, 0.4, or 40% instead.
References
Resources
- Photo Credit red dice image by Tammy Mobley from Fotolia.com
