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How Probability Is Calculated

Imagine you are at the state fair or at an amusement park, and that you to play the wheel of fortune. You can win small and large chocolate prizes.

Chocolate wheel of fortune

The wheel starts to spin. There’s only one field on the wheel that wins you the biggest chocolate prize. In total, there are 12 different fields on the wheel that can stop under the pin. What’s the probability that you win the biggest chocolate?

Probabilities are often written as fractions. You must therefore find out what should be in the numerator, and what should be in the denominator. The numerator states the number of possibilities that will win you the biggest chocolate. In this case, there’s only one place the wheel can stop at to give you the biggest prize. Therefore, it should say 1 in the numerator. The denominator states the total number of outcomes, which in this case is the number of fields that can stop under the pin. There are 12 different possibilities, so it must say 12 in the denominator. The probability that you win the biggest chocolate is therefore 1 12.

Rule

When we are absolutely sure that something will happen, we say the probability is equal to 1, which is the same as 100 %.

When we are absolutely sure that something will not happen, we say the probability is equal to 0, which is the same as 0 %.

The probability of something happening is between 0 and 1, as in the case with the prize wheel. The closer to 1 the probability is, the more likely the event is to occur.

Think About This

In the example with the prize wheel, there was only one option that gave you the biggest chocolate. Yet, there were three other fields on the wheel that would have given you smaller chocolates. What is the probability that you get a chocolate as a prize regardless of its size?

The numerator must be the number of outcomes that give you a prize. There are four fields on the wheel that give you a prize: One field wins you the big chocolate, and three fields win you smaller chocolates. Therefore, it should say 4 in the numerator.

The denominator must state how many possible outcomes there are. There are still 12 different fields that can stop under the pin. Therefore, it should say 12 in the denominator. The probability of winning a chocolate prize (small or large), is then 4 12 = 1 3.

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