Probability Calculator

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Coincidences are a funny thing. They make you think, “What are the odds?!” If you’re interested in odds, you’ll definitely enjoy using our Probability Calculator!

What Is a Probability?

In layman’s terms, a probability is how likely something is to happen. This is expressed mathematically by dividing the number of ways something can happen by the total number of possible outcomes.

Probabilities are used in everyday life. We use it to gauge the odds of something happening. One example is when we hear the weatherman say that there’s an 80% chance of rain. 80% is quite high, so we prepare for the worst by bringing an umbrella when we go out.

Likewise, when the weatherman says there’s only a 20% chance of rain, we may bring an umbrella if we want to be extra sure. However, those who prefer to go by the odds probably won’t bother with an umbrella.

Gamblers who play card games also love calculating probabilities. They know that there is one chance in 52 of drawing a specific card, so they like to bet on those odds. It’s the same for those who bet on the roulette. There’s always a 50% chance of landing on either a black slot or a red slot.

We use probabilities to deal with uncertainties. While we can never be absolutely sure about what will happen, probabilities allow us to prepare for the likeliest situation.

How to Calculate for Probability: The Basics

Let’s take the example of rolling a die. What is the probability that you’ll get a “2” with one roll?
There is only one face with a “2” on it, so it can only happen once per roll. As for the total number of outcomes, there are 6 faces on one die, so the value is 6.

The probability of rolling a “2” is 1 chance out of 6 or 1/6. This gives you a value of 0.1666~.
Probabilities are expressed in percentages. A 100% probability means you get the desired outcome all the time. A 50% probability means you get the desired outcome only half the time. A 0% probability means you never get the desired outcome.

In the case of rolling a die and getting a “2”, you multiply 0.1666~ by 100 to get a percentage value. This gives you a 16% probability.

Probabilities of Single Events

When you use the Probability Calculator, you can find out the relationship between two probabilities.

Taking the example of dice, let’s say you have a pair. You want to know the probabilities surrounding rolling a “2” and rolling a “3”. Let’s call the probability of rolling a “2” P(A) and the probability of rolling a “3” P(B). As discussed above, the odds of rolling the dice and getting a specific result is 16 times out of 100 tries or 16%.

P(A) = 16%
P(B) = 16%

When you input these values into a calculator, you immediately get a list of other results about the relationship between these two probabilities.
P(A∩B) is the probability of both P(A) and P(B) occurring.
 This is calculated by multiplying the probabilities together:

P(A∩B) = P(A) x P(B)
 = 16% x 16%
 = 2.56%

This is essentially saying that you have very low odds of rolling both a “2” and a “3” at the same time. 
Now, if you want to know the probability that you’ll either roll a “2” or a “3”, you are searching for the value of P(A∪B). To get the value of P(A∪B), you must add the probability of P(A) and P(B) and subtract this by the probability of rolling both a “2” and a “3”.

P(A∪B) = P(A) + P(B) - P(A ∩ B)
 = 16% + 16% - 2.56%
 = 29.44%

This shows that you have decent odds of rolling either a “2” or a “3”.

Probabilities for Calculating for a Series of Events

While it’s good to know the odds of something happening one time, you might also want to know the probability of an event happening multiple times. The Probability Calculator also has this automatic function.

You only need to input the number of times you wish to repeat an event. As with the example above, let’s use the probability of rolling a “2” or a “3”.

We already know the probability of rolling the dice and getting only one desired result, at least one desired result, and both desired results. Now let’s find out the odds of it happening over a series of rolls.

In the “when trying” field, you put in the number of times you want to roll the dice. The values that appear show you the probabilities. In the calculation, this is the exponent you’ll use to multiply the probability.

For example, you want to know the probability of rolling a “2” 4 times in a row. This is expressed with this equation:

 = P(A)4
 = 16%4
 = 0.065536%

This very small value is the value that appears in the “A always occurring” field.

For the “A never occurring” field, the computation for this is:

= P(B')4
= 84%4
= 49.7871%

This means you have an almost 50% chance that the dice won’t land on either “2” or “3”!
Let the Probability Calculator help you find out the likelihood of a certain outcome. When you know the odds, that makes your decision all the easier!

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