The sample space is a set of all possible outcomes for an event. A sample space can be small, such as the 2 outcomes when a coin is flipped. Or a sample space can be large, such as the possible number of Texas Classic automobile license plates.

Identifying the sample space can help us to calculate the probability of an event.

The formula given below can be used to find probability of an event.

**Example 1 :**

What is the probability of rolling an even number on a standard number cube ?

**Solution : **

**Step 1 :**

Find the sample space for a standard number cube.

There are 6 possible outcomes.

S = {1, 2, 3, 4, 5, 6}

**Step 2 :**

Find the number of ways to roll an even number.

The event can occur 3 ways.

{2, 4, 6}

**Step 3 :**

Find the probability of rolling an even number.

Substitute values and simplify.

P(even) = 3/6

P(even) = 1/2

The probability of rolling an even number is 1/2.

**Example 2 :**

What is the probability picking a purple marble from a jar with 10 green and 10 purple marbles.

**Solution : **

**Step 1 :**

Find the sample space for a standard number cube.

There are 20 possible outcomes.

10 Green marbles and 10 Purple marbles

**Step 2 :**

Find the number of ways to pick a purple marble.

The event can occur in 10 ways.

Because we have ten purple marbles.

**Step 3 :**

Find the probability of picking a purple marble.

P (purple) = No. of purple marbles / Total no. of marbles

Substitute values and simplify.

P (purple) = 10 / 20

P (purple) = 1/2

The probability of picking a purple marble is 1/2.

**Example 3 :**

What is the probability of rolling a number greater than 4 on a standard number cube ?

**Solution : **

**Step 1 :**

Find the sample space for a standard number cube.

There are 6 possible outcomes.

S = {1, 2, 3, 4, 5, 6}

**Step 2 :**

Find the number of ways to roll a number greater than 4.

The event can occur 2 ways.

{5, 6}

**Step 3 :**

Find the probability of rolling a number greater than 4.

P ( > 4 ) = No. of numbers > 4 / Total no. of numbers

Substitute values and simplify.

P ( > 4 ) = 2 / 6

P ( > 4 ) = 1/3

The probability of rolling a number greater than 4 is 1/3.

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

If you have any feedback about our math content, please mail us :

**v4formath@gmail.com**

We always appreciate your feedback.

You can also visit the following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**