How to Solve Probability Problems

Are probability problems causing problems for you? Well you're not alone. Statistics and probability homework have been known to cause headaches in 1 out of every 10 students. Probability is a tough subject to tackle at first glance. Let's break down some examples and learn how to solve probability problems.

What Is Probability?
In it's simplest definition, probability is the number of times an event is true, divided by the number of possible outcomes. An easy way to illustrate this is to use a die, like the ones you use to play Monopoly. A regular die has six sides numbered one through six. If you rol the die, the number of times that it will land on the number one on any given roll is divided by the number of possible outcomes. In this case, there are six possible outcomes, one for each of the die-s sides, so your probability of rolling a one is one in six.

Finding Probability Solutions
In order to solve any probability problem, you simply take the number of times an event can be true and divide it by the total number of outcomes. Probability analysis always follows the die example, but it gets more complicated as the number of possible outcomes increases.

Say you have two dice. If you roll the dice at the same time, what is the probability of them both landing on the number? First you need to calculate how many possible outcomes there are. If you think about it logically, you could roll a 1 and 2, a 1 and a 3, a 1 and a 4, etc. These are known as combinations.

It will really help if you visualize it, so to make things easier, you can make a table of all the possible combinations. It should look like the one below:

1 + 1

1 + 2

1 + 3

1 + 4

1 + 5

1 + 6

2 + 1

2 + 2

2 + 3

2 + 4

2 + 5

2 + 6

3 + 1

3 + 2

3 + 3

3 + 4

3 + 5

3 + 6

4 + 1

4 + 2

4 + 3

4 + 4

4 + 5

4 + 6

5 + 1

5 + 2

5 + 3

5 + 4

5 + 5

5 + 6

6 + 1

6 + 2

6 + 3

6 + 4

6 + 5

6 + 6

 

Count the number of squares in the grid. This is the total number of possible outcomes. It should total 36. Count the number of squares that both dice show a 1. You can see that your probability of rolling two ones is 1 in 36.

You don't need to make a grid to solve the problem, it just helps you to see the poential outcomes. To quickly solve the above problem, you can use multiplication. You already know the probability of rolling a one on a single die is one in six. The odds of rolling a one on the other die are one in six as well. So you can multiply 1/6 by 1/6 and get the same answer: 1/36.

Probability can get a lot more complicated, but if you take the problem and break it down to it's simplest terms and remember the basics, you should be able to solve it.

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