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How to Determine Probability: Formulas and Samples

What Is Probability?

Probability essentially refers to the likelihood of something happening. Because maths is not quite as scientifically exact as we’d like it to be when predicting future events and outcomes, we instead refer to the probability of something happening. We make an educated guess.

statistical data analysis schema

Take a coin for example. When we flip a coin into the air, there is a 50/50 chance that the coin will land on Heads and a 50/50 chance that it will land on Tails. This is because there are only two possible outcomes. The less possible outcomes, the greater the probability of one of them occurring. In other words, the odds are on each side.

Conversely, when we toss a dice, there are now six possible results. This means that there is a 1/6 probability that it will land on either 1,2,3,4,5,6.

How To Determine Probability


Formula: ————————————————

Total Number of Possible Outcomes

To determine probability, you need to pick an event. For example, you might want to determine the probability of a dice landing on the number four.

Then you need to define the total number of possible outcomes. Because there are six sides on a dice, your total number of possible outcomes is six.

You need to then divide your event by the total number of possible outcomes. Because there is only one number four on your dice, this means that you divide 1 by 6:1

Probability of rolling the number 3 on a dice: — 6

To use another example, imagine that you’re trying to figure out how to determine probability of a football team winning. Because there are three results that can occur in a football match, win, lose, or draw, the probability of a football team winning is: 1—3

Counting Techniques In Probability

Counting techniques in probability can be really simple. Let’s say that you own 4 trousers and 3 sweaters and you’re wondering how many various outfits are open to you.

4 x 3 = 12 various outfits.

But then let’s say that you want to know how to count probability when it comes to determining how many different combinations you can wear if you bought 5 new hats.

4 x 3 x 2 = 24 different outfits.

Counting techniques in probability also extend to choices that are dependent on one another.

So far we have looked at how to count probability with choices that are independent of one another. For example, you can wear any t-shirt with any pair of trousers, just like you can wear any hat with any t-shirt or trousers

But let’s say you’re looking to buy a BMW.

2 body styles are open to you: hatchback and coupe.

5 colours are available: black, silver, green, blue and red.

3 models are available: Sport, standard, and luxury.

In this case, though, you’re not allowed to purchase a red coupe because BMW don’t produce red coupe’s. So we have to alter the formula:

5 x 3 + 4 x 3 = 15


15 + 12 = 27

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